### Examination Questions in Geometry - Triangles

1. For a triangle ABC, D and E are two points on AB and AC such that AD = 1/4AB, AE = 1/4AC. If BC = 12 cm then DE is :

1. 3 cm
2. 6 cm
3. 5 cm
4. 4 cm

2. In an acute angled triangle ABC, if sin 2(A + B – C)= 1 and tan(B + C – A) = √3, then the value of angle B is

1. 60°
2. 30°
3. 52 ½°
4. 67 ½°

3. If the in radius of a triangle with perimeter 32 cm is 6 cm, then the area of the triangle in sq. cm is

1. 48
2. 100
3. 64
4. 96

4. ABC is a right angled triangle, B being the right angle. Mid-points of BC and AC are respectively B’ and A’. The ratio of the area of the quadrilateral AA’ B’B to the area of the triangle ABC is

1. 1 : 2
2. 2 : 3
3. 3 : 4
4. None of the above

5. In a triangle ABC, the side BC is extended up to D. Such that CD = AC, if angle BAD = 109° and angle ACB = 72° then the value of angle ABC is

1. 35°
2. 60°
3. 40°
4. 45°

6. Side BC of triangle ABC is produced to D. If angle ACD = 140o and angle ABC = 3 ⁄BAC, then find angle A.

1. 45°
2. 55°
3. 35°
4. 60°

7. If O be the circum centre of a triangle PQR and angle QOR = 110°, angle OPR = 25°, then the measure of angle PRQ is

1. 55°
2. 60°
3. 65°
4. 50°

8. D and E are mid-points of AB and AC of triangle ABC. If angle A = 80o, angle C = 35o, then angle EDB is equal to

1. 100°
2. 115°
3. 120°
4. 125°

9. In a right-angled triangle ABC, angle ABC = 90°, AB = 5 cm and BC = 12 cm. The radius of the circum circle of the triangle ABC is

1. 6.5 cm
2. 7 cm
3. 7.5 cm
4. 6 cm

10. If the circum radius of an equilateral triangle ABC be 8 cm, then the height of the triangle is

1. 8 cm
2. 12 cm
3. 16 cm
4. 6 cm