Geometry (Part-13)

Total Questions: 35

1. Vertices A, B, C and D of a quadrilateral ABCD lie on a circle. ∠A is three times ∠C and ∠D is two times ∠B . What is the difference between the measures of ∠D and ∠C ? [SSC CGL 23/08/2021 (Morning)]

Correct Answer: (c) 75º
Solution:

2. In ∆ABC, D is a point on BC such that ∠BAD = 1/2 ∠ADC and ∠BAC = 77º and ∠C = 45º, What is the measure of ∠ADB ? [SSC CGL 23/08/2021 (Afternoon)]

Correct Answer: (a) 64°
Solution:

3. In the triangle ABC, D and E are mid-points of AB and BC respectively. If area (∆CED) = 8cm², then what is the area (ADEC) in cm²? [SSC CGL 23/8/2021 (Afternoon)]

Correct Answer: (c) 24
Solution:

4. Triangles ABC and DBC are right angled triangles with common hypotenuse BC. BD and AC intersect at P, when produced. If PA = 8 cm, PC = 4 cm and PD = 3.2 then the length of BD, in cm, is: [SSC CGL 23/08/2021 (Evening)]

Correct Answer: (d) 6.8
Solution:

5. ABCD is a cyclic quadrilateral in which ∠A = x°, ∠B = 5yº, ∠C = 2xº and ∠D = y°. What is the value of (3x - y) ? [SSC CGL 23/08/2021 (Evening)]

Correct Answer: (d) 150°
Solution:

6. In a triangle ABC, length of the side AC is 4 cm more than 2 times the length of the side AB. Length of the side BC is 4 cm less than the three times the length of the side AB. if perimeter of △ABC is 60 cm, then its area (in cm²) is: [SSC CGL 24/08/2021 (Morning)]

Correct Answer: (a) 120
Solution:

7. The vertices of a ∆ABC lie on a circle with centre O. AO is produced to meet the circle at the point P. D is a point on BC such that AD ⊥ BC. If ∠B = 68º and ∠C = 52º, then the measure of ∠DAP is: [SSC CGL 24/08/2021 (Morning)]

Correct Answer: (b) 16°
Solution:

8. The area of table top in the shape of an equilateral triangle is 9√3 cm². What is the length (in cm) of each side of the table? [SSC CGL 24/08/2021 (Morning)]

Correct Answer: (a) 6
Solution:

Area of equilateral triangle

9. In a circle with centre O, AB is a chord of length 10 cm. Tangents at points A and B intersect outside the circle at P. If OP = 2OA then find the length (in cm) of AP. [SSC CGL 24/08/2021 (Afternoon)]

Correct Answer: (a) 10
Solution:

10. In ΔABC and ∆DEF, we have AB/DF = BC/DE = AC/EF, then which of the following is true ? [SSC CGL 24/08/2021 (Afternoon)]

Correct Answer: (b) ΔBCA ~ ΔDEF
Solution: