Geometry (Part-12)

Total Questions: 50

1. In the following figure, P and Q are centers of two circles. The circles are intersecting at points A and B. PA produced on both the sides meets the circles at C and D. If ∠CPB = 100º , then find the value of x. [SSC CGL 18/04/2022 (Morning)]

Correct Answer: (d) 100
Solution:

2. A circle is inscribed in ∆ABC, touching AB, BC and AC at points P, Q and R, respectively. If AB - BC = 4cm, AB - AC = 2cm, and the perimeter of ∆ABC = 32 cm, then AC (in cm) = ? [SSC CGL 18/04/2022 (Morning)]

Correct Answer: (c) 32/3
Solution:

3. In a ∆ABC D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 14.4cm. CA = 15.2 cm and AB 12.4 cm, what is the perimeter of the ∆DEF? [SSC CGL 19/04/2022 (Morning)]

Correct Answer: (c) 21
Solution:

4. Let ∆ABC ~ ∆QPR and (Area of ∆ABC): (Area of ∆PQR) = 121 : 64. If QP 14.4 cm, PR 12 cm and AC = 18 cm. Then what is the length of AB (in cm)? [SSC CGL 19/04/2022 (Morning)]

Correct Answer: (c) 19.8
Solution:

5. The circumcenter of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes? [SSC CGL 19/04/2022 (Afternoon)]

Correct Answer: (a) 9.6
Solution:

Perpandicular to the base of a triangle from circumcenter is inradius

6. AB is a chord of a circle with centre O. C is a point on the circumference of the circle in the minor sector. If ∠ABO = 40°. what is the measure (in degree) of ∠ACB ? [SSC CGL 19/04/2022 (Afternoon)]

Correct Answer: (b) 130°
Solution:

7. In a circle with centre O and radius 13 cm, and two parallel chords are drawn on different sides of the centre.If the length of one chord 10cm and the distance between two chords is 17cm, then find the difference in length of the two chords (in cm) [SSC CGL 19/04/2022 (Evening)]

Correct Answer: (b) 14
Solution:

8. In a circle with center O, PA and PB are tangents to the circle at point A and point B, respectively, C is a point on the major arc AB, If ∠ACB = 50°, then find the measure of ∠APB. [SSC CGL 20/04/2022 (Morning)]

Correct Answer: (c) 80°
Solution:

9. In a right triangle ABC, right angle at B, altitude BD is drawn to the hypotenuse AC of the triangle. If AD = 6 cm, CD = 5cm, then find the value of AB² + BD² (In cm²) [SSC CGL 20/04/2022 (Morning)]

Correct Answer: (b) 96
Solution:

10. AC is the diameter of a circle dividing the circle into two semicircles. ED is a chord in one semicircle, such that ED is parallel to AC, B is a point on the circumference of the circle in the other circumference ∠CBE = 75°, what is the measure (in degree) of ∠CED? [SSC CGL 20/04/2022 (Afternoon)]

Correct Answer: (d) 15°
Solution: