Geometry

Total Questions: 50

1. From a point T, a tangent TP at point P, is drawn to a circle with centre O. A secant TQR (point Q is near to point T) is drawn from the point T. △PQR is inscribed into the circle by joining the points P, Q and R. Draw lines OQ and OR. If ∠PTQ is 27° and TPQ = 55° what is the degree measure of angle ∠ROQ [SSC CGL 25/09/2024 (3rd Shift)]

Correct Answer: (a) 86
Solution:

2. AB is the chord of the circle with centre O. A line segment DOC originating from a point D on the circumference of the circle in the major segment meets AB produced at C such that BC = OD If angle BCO = 30°, then angle AOD is: [SSC CGL 23/09/2024 (2nd Shift)]

Correct Answer: (b) 90°
Solution:

3. A triangle ABC is made on a circle, where AB is the diameter of the circle. If BC is equal to the radius of the circle and angle ABC =x ∠BAC then x is: [SSC CGL 23/09/2024 (1st Shift)]

Correct Answer: (b) 2
Solution:

4. AB is a chord of length 32 cm of a circle of radius 20 cm, the tangents at A and B intersect at a point T. Find length TA (rounded off to two digits after decimal). [SSC CGL 19/09/2024 (1st Shift)]

Correct Answer: (c) 26.67 cm
Solution:

5. WXYZ is a quadrilateral in which XQ and ZP are perpendicular to WY such that XQ = ZP. Diagonals ZX and WY intersect each other at point O. If OX = 12 cm, then find the value of ZX (in cm). [SSC CGL 19/09/2024 (1st Shift)]

Correct Answer: (b) 24
Solution:

6. In triangle ABC, D is the mid-point of BC. If DL perpendicular to AB and DM perpendicular to AC such that DL = DM, then the triangle will be: [SSC CGL 17/09/2024 (3rd Shift)]

Correct Answer: (a) isosceles triangle
Solution:

7. Solve it- [SSC CGL 12/09/2024 (3rd Shift)]

Correct Answer: (d) 2:1
Solution:

8. If the length of a common external tangent to two circles is 9 and that of a common internal tangent is 5, then the product of the radii of the two circles is: [SSC CGL 10/09/2024 (3rd Shift)]

Correct Answer: (c) 14
Solution:

9. X, Y, and Z are three points on a plane with XY = 11 cm, YZ = 13 cm, and XZ = 24 cm. The number of circles that travel through points X, Y, and Z is: [SSC CGL 10/09/2024 (1st Shift)]

Correct Answer: (a) 0
Solution:

10. In an obtuse-angled triangle ABC, the length of its longest side AB is 50 cm and one of the other two sides are 42 cm. If the area of the triangle is 294 cm², what is the length (in cm) of its third side? [SSC CHSL 11/07/2024 (4th Shift)]

Correct Answer: (d) 2√58
Solution: