Geometry Test for SSC CGL

ABCD is a cyclic quadrilateral in which ∠A = x°, ∠B = 5y°, ∠C = 2x° and ∠D = y°. What is the value of (3x - y)?

AB is the diameter of a circle with centre O. C and D are two points on the circumference of the circle on either side of AB, such that ∠CAB = 42° and ∠ABD = 57°. What is difference (in degrees) between the measures of ∠CAD and ∠CBD?

In the following figure, MN is a tangent to a circle with centre O at point A. If BC is a diameter and ∠ABC = 42°, then find the measure of ∠MAB.

If PAB is a secant of a circle and PT is a tangent drawn from an exterior point. If PA = 3 cm and PT = 6 cm, then AB is

Two chords AB and CD of a circle when produced, meet at a point P outside the circle. If AB = 6 cm, PB = 5 cm, PD = 4 cm, then CD is equal to:

Chord AB of a circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P., then the length of the tangent AP (in cm) is:

In the given figure, MP is tangent to a circle with centre A and NQ is a tangent to a circle with centre B. If MP = 15 cm. NQ = 8 cm. PA = 17 cm and BQ = 10 cm, then AB is:

In ΔPQR, ∠Q = 66° and ∠R = 34 ° . T is a point on QR , and S is a point between Q and T such that PS ⊥ QR and PT is the bisector of ∠QPR. What is the measure of ∠SPT?

What is the reflection of the point (4, -3) in the line y = 1?

Centre of two concentric circles is O. The areas of the two circles are 616 cm$^2$ and 154 cm$^2$ respectively. A tangent is drawn through point A on the larger circle to the smaller circle. This tangent touches the small circle at B and intersects the larger circle at C. What is the length (in cm) of AC?