Chord AB of 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:

If C₁, C₂ be the centres of rwo circles and r₁, r₂ be the respective radii such that the distance between the centres is equal to the sum of the radii of the two circles, find the number of common tangents.

If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA then.

A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is

Angle subtended by a chord AB on the centre of the circle is 140 degree. What will be the angle subtended by the chord AB on the major are of the circle? 

In the figure, XYZ is a secant. and ZT is a tangent to the circle at T. If TZ = 12 cm and YZ = 8 cm, then find the length of XY.

ABC is a triangle in which DE || BC and AD: DB = 5: 4. Then DE: BC is

In △ABC, D and E are points on sides AB and AC, such that DE||BC. If AD=x+3, DB=2x-3, AE=x+1 and EC=2x-2, then the value of x is