A, B, C are three points on a circle having centre O. If angle OAC = 25° and angle OBC = 35°, then find the size of angle AOB.

ABCD is a cyclic quadrilateral, AB is a diameter of the circle. If angle ACD = 50° , the value of angle BAD is _________

Two circles of equal radii touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. What is the relation between TQ and TR?

O is the centre of the circle passing through the points A, B and P such that angle PAO = 30°, angle PBO = 40° and angle AOB = x. What is the value of x?

In a triangle ABC, D and E are two points on AB and AC such that AD = 1/4AB, AE = 1/4AC. If BC = 12 cm then DE is ______

In an acute angled triangle ABC, if sin 2(A + B – C)= 1 and tan(B + C – A) = √3, find the value of angle B.

In a triangle ABC, the side BC is extended up to D. Such that CD = AC, if angle BAD = 109° and angle ACB = 72°, find the value of angle ABC.

In a right-angled triangle ABC, angle ABC = 90°, AB = 5 cm and BC = 12 cm. The radius of the circumcircle of the triangle ABC is ______

D and E are mid-points of AB and AC of triangle ABC. If angle A = 80°, angle C = 35°, find angle EDB.