O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP? 

An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor are BC and ∠CBD=40⁰. Find the measure of ∠BCD.

In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28° and BD = DC. What is the measure of ∠BOC?

In ΔABC, D and E are points on the sides AB and AC, respectively, such that DE || BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is:

The sides BA and DE of a regular pentagon are produced to meet at F. What is the measure of ∠EFA?

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? 

AB is a chord of a circle in minor segment with center O.C is a point on the minorarc of the circle between the points A and B. The tangents to the circle at A and B meet at the point P. If ∠ACB = 102⁰ , then what is the measure of ∠APB?

If the orthocenter and the centroid of a triangle are the same, then the triangle is: