This is the Multiple Choice Questions Part 1 of the Series in Plane Geometry topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

### Multiple Choice Questions Topic Outline

- MCQs in Venn Diagram | MCQs in Definition of Plane Geometry | MCQs in Angles | MCQs in Circles | MCQs in Ellipse | MCQs in Polygons | MCQs in Triangles | MCQs in Quadrilaterals | MCQs in Trapezoids and Trapeziums | MCQs in Parallelograms | MCQs in Square and Rectangles | MCQs in Rhomboid and Rhombus

### Online Questions and Answers in Plane Geometry Series

Following is the list of multiple choice questions in this brand new series:

**Plane Geometry MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

**MCQs from Number 51 – 100**Answer key:

**PART II**

**MCQs from Number 101 – 150**Answer key:

**PART III**

### Start Practice Exam Test Questions Part I of the Series

**Choose the letter of the best answer in each questions.**

**Problem 1: ECE Board November 1998**

Find the angle in mills subtended by a line 10 yards long at a distance of 5000 yards.

- A. 1
- B. 2
- C. 2.5
- D. 4

**Problem 2: ECE Board April 1999**

Assuming that the earth is sphere whose radius is 6400 km. Find the distance along a 3 degree arc at the equator of the earth’s surface.

- A. 335.10 km
- B. 533.10 km
- C. 353.10 km
- D. 353.01 km

**Problem 3: EE Board April 1992**

The angle subtended by an arc is 24o. If the radius of the circle is 45 cm, find the length of arc

- A. 16.85 cm
- B. 17.85 cm
- C. 18.85 cm
- D. 19.85 cm

**Problem 4: ME Board April 1990**

A rat feel on a bucket of a water wheel with diameter of 600 cm which travelled an angle of 190obefore it dropped from the bucket. Calculate for the linear cm that the rat was carried by the bucket before it fell.

- A. 950
- B. 965
- C. 985
- D. 995

**Problem 5: ECE Board November 1992**

Given the circle whose diameter AB equals 2 m. If two points C and D lie on the circle and angles ABC and BAD are 18o and 36o, respectively, find the length of the major arc CD.

- A. 1.26 m
- B. 1.36 m
- C. 1.63 m
- D. 1.45 m

**Problem 6:**

A certain angle has as supplement 5 times its complement. What is the angle?

- A. 67.5o
- B. 58.5o
- C. 30o
- D. 27o

**Problem 7: ECE Board November 1998**

Each angle of a regular dodecagon is equal to

- A. 135o
- B. 150o
- C. 125o
- D. 105o

**Problem 8: CE Board May 1997**

How many sides has a polygon if the sum of the interior angles is 1080o?

- A. 5
- B. 6
- C. 7
- D. 8

**Problem 9: ECE Board March 1996**

The sum of the interior angles of a polygon is 540o. Find the number of sides.

- A. 3
- B. 4
- C. 5
- D. 6

**Problem 10: ECE Board April 1991**

Find the sum of the interior angles of the vertices of a five pointed star inscribed in a circle.

- A. 150o
- B. 160o
- C. 170o
- D. 180o

**Problem 11: ME Board April 1999**

How many sides are in a polygon if each interior angle is 165 degrees.

- A. 12
- B. 24
- C. 20
- D. 48

**Problem 12:**

How many diagonals are there in a polygon of 20 sides?

- A. 200
- B. 170
- C. 100
- D. 158

**Problem 13: ME Board April 1999**

Find each interior angle of a hexagon.

- A. 90o
- B. 120o
- C. 150o
- D. 180o

**Problem 14: EE Board April 1994**

Given a triangle, C = 100o, A = 15 m, B = 20 m. Find C.

- A. 26 m
- B. 27 m
- C. 28 m
- D. 29 m

**Problem 15: CE Board November 1994**

In triangle ABC, angle A = 45o and C = 70o. The side opposite angle C is 40 m long. What is the length of the side opposite angle A?

- A. 26.1 m
- B. 27.1 m
- C. 29.1 m
- D. 30.1 m

**Problem 16: CE Board May 1995**

In triangle ABC, angle C = 70o, A= 45o, AB = 40 m. What is the length of the median drawn from vertex A to side BC?

- A. 36.3 m
- B. 36.6 m
- C. 36.9 m
- D. 37.2 m

**Problem 17: EE Board April 1991**

From a point outside of an equilateral triangle, the distances to the vertices are 10 m, 18 m and 10 m, respectively. What is the length of one side of a triangle?

- A. 17.75 m
- B. 18.50 m
- C. 19.95 m
- D. 20.50 m

**Problem 18: EE Board April 1991**

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the inscribed circle.

- A. 2.25 cm
- B. 2.35 cm
- C. 2.45 cm
- D. 2.55 cm

**Problem 19: CE Board May 1996**

What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm.?

- A. 12.73 m
- B. 13.52 m
- C. 14.18 m
- D. 15.55 m

**Problem 20: EE Board April 1991**

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the circumscribing circle.

- A. 7.14 cm
- B. 7.34 cm
- C. 7.54 cm
- D. 7.74 cm

**Problem 21: CE Board May 1996**

Two sides of a triangle are 50 m and 60 m long. The angle included between these sides is 30o. What is the interior angle opposite the longest side?

- A. 93.74o
- B. 92.74o
- C. 90.74o
- D. 86.38o

**Problem 22: ECE Board March 1996**

A circle with radius 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border.

- A. 1.76 cm
- B. 1.35 cm
- C. 1.98 cm
- D. 2.03 cm

**Problem 23: ME Board April 1996**

The area of a circle is 89.42 sq. inches. What is its circumference?

- A. 32.25 in.
- B. 33.52 in.
- C. 35.33 in.
- D. 35.55 in.

**Problem 24: ECE Board April 1991**

A square section ABCD has one of its sides equal to x. Point E is inside the square forming an equilateral triangle BEC having one side equal in length to the side of the square. Find the angle AED.

- A. 130o
- B. 140o
- C. 150o
- D. 160o

**Problem 25: CE Board November 1995**

The area of a circle circumscribing about an equilateral triangle is 254.47 sq. m. What is the area of the triangle in sq. m?

- A. 100.25
- B. 102.25
- C. 104.25
- D. 105.25

**Problem 26: CE Board May 1995**

What is the area in sq. cm of the circle circumscribed about an equilateral triangle with a side 10 cm long?

- A. 104.7
- B. 105.7
- C. 106.7
- D. 107.7

**Problem 27: CE Board November 1992**

The area of a triangle inscribed in a circle is 39.19 cm2 and the radius of the circumscribed circle is 7.14 cm. If the two sides of the inscribed triangle are 8 cm and 10 cm, respectively, find the third side.

- A. 11 cm
- B. 12 cm
- C. 13 cm
- D. 14 cm

**Problem 28: CE Board November 1994**

The area of a triangle is 8346 sq. m and two of its interior angles are 37o25’ and 56o17’. What is the length of the longest side?

- A. 171.5 m
- B. 181.5 m
- C. 191.5 m
- D. 200.5 m

**Problem 29: ECE Board April 1998**

The angle of a sector is 30o and the radius is 15 cm. What is the area of the sector in cm2?

- A. 59.8
- B. 89.5
- C. 58.9
- D. 85.9

**Problem 30: EE Board April 1992**

Two perpendicular chords both 5 cm from the center of a circle divide the circle into four parts. If the radius of the circle is 13 cm, find the area of the smallest part.

- A. 30 cm2
- B. 31 cm2
- C. 32 cm2
- D. 33 cm2

**Problem 31: ECE Board April 1998**

The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. The area of the largest circle is?

- A. 72 π
- B. 23 π
- C. 64 π
- D. 16 π

**Problem 32: ECE Board November 1993**

The arc of a sector is 9 unites and its radius is 3 units. What is the area of the sector in square units?

- A. 12.5
- B. 13.5
- C. 14.5
- D. 15.5

**Problem 33: CE Board May 1998**

A circle having an area of 452 sq. m is cut into two segments by a chord which is 6 m from the center of the circle. Compute the area of the bigger segment.

- A. 354. 89 sq. m
- B. 363. 68 sq. m
- C. 378. 42 sq. m
- D. 383. 64 sq. m

**Problem 34: ECE Board April 1992**

A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of the circles has a radius of 9 m and each circle passes through the center of the other. Find the area of the swimming pool.

- A. 380 m2
- B. 390 m2
- C. 400 m2
- D. 410 m2

**Problem 35: ME Board April 1991**

Find the difference of the area of the square inscribe in a semi-circle having a radius of 15 ,. The base of the square lies on the diameter of the semi-circle.

- A. 171.5 cm2
- B. 172.5 cm2
- C. 173.5 cm2
- D. 174.5 cm2

**Problem 36: ECE Board November 1995**

A rectangle ABCD which measures 18 cm. by 24 cm. is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.

- A. 20.5 cm2
- B. 21.5 cm2
- C. 22.5 cm2
- D. 23.5 cm2

**Problem 37: ECE Board April 1998**

A trapezoid has an area of 36 m2 and an altitude of 2 m. Its two bases have the ration of 4:5. What are the lengths of the bases?

- A. 12, 15
- B. 7, 11
- C. 8, 10
- D. 16, 20

**Problem 38: EE Board March 1998**

A rhombus has diagonals of 32 and 20 inches. Determine its area.

- A. 360 in2
- B. 280 in2
- C. 320 in2
- D. 400 in2

**Problem 39: ECE Board April 1998**

If the sides of a parallelogram and an included angle are 6, 10 and 100o, respectively, find the length of the shorter diagonal.

- A. 10.63
- B. 10.37
- C. 10.73
- D. 10.23

**Problem 40: CE Board November 1996**

Find the area of a quadrilateral having sides AB = 10 cm, BC = 5 cm, CD = 14.14 cm and DA = 15 cm, if the sum of the opposite angles is equal to 225o.

- A. 96 sq. m
- B. 100 sq. m
- C. 94 sq. m
- D. 98 sq. m

**Problem 41: EE Board October 1992**

Determine the area of the quadrilateral shown, OB = 80 cm, AO = 120 cm, OD = 150 cm and ϕ = 25o

- A. 2721.66 cm2
- B. 2271.66 cm2
- C. 2172.66 cm2
- D. 2217.66 cm2

**Problem 42: CE Board October 1997**

Find the area of a quadrilateral have sides 12 m, 20 m, 8 m and 16.97 m. If the sum of the opposite angles is equal to 225o, find the area of the quadrilateral.

- A. 100 m2
- B. 124 m2
- C. 168 m2
- D. 158 m2

**Problem 43: ME Board October 1996, ME Board April 1997**

The area of a regular hexagon inscribed in a circle of radius 1 is?

- A. 1.316
- B. 2.945
- C. 2.598
- D. 3.816

**Problem 44: EE Board April 1990**

Find the area (in cm2) of a regular octagon inscribed in a circle of radius 10 cm?

- A. 283
- B. 289
- C. 298
- D. 238

**Problem 45: GE Board February 1992**

A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle formed by the sides of the hexagon.

- A. 36. 45 sq. m
- B. 63. 54 sq. m
- C. 45. 63 sq. m
- D. 54. 36 sq. m

**Problem 46: EE Board April 1993**

Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.

- A. 1075 m2
- B. 1085 m2
- C. 1080 m2
- D. 1095 m2

**Problem 47: ME Board October 1996**

The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle?

- A. 5.533 in.
- B. 5.335 in.
- C. 6.335 in.
- D. 7.335 in.

**Problem 48: EE Board April 1990**

In a circle of diameter of 10 m, a regular five-pointed star touching its circumference is inscribed. What is the area of that part not covered by the star?

- A. 40. 5 sq. m
- B. 45. 5 sq. m
- C. 50. 5 sq. m
- D. 55. 5 sq. m

**Problem 49: EE Board March 1998**

A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the large pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.

- A. 430.70 cm3
- B. 573.26 cm3
- C. 473.77 cm3
- D. 516.14 cm3

**Problem 50: EE Board March 1999**

Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.

- A. 441.66 cm2
- B. 467.64 cm2
- C. 519.60 cm2
- D. 493.62 cm2