In the given figure, centre of two circles is O. Chord AB of bigger
circle intersects the smaller circle in points P and Q .
Show that AP = BQ.

A circle with centre C touches the circle with centre D internally in the point E. Point D lies on the smaller circle. Chord EB of the external circle intersects internal circle at point A. Prove that seg EA~=seg AB

In the adjoining figure, circles with centres X and Y touch internally at point Z. Seg BZ is a chord of bigger circle and it intersects smallest circle at point A. prove that, seg AX || seg BY.

In the adjoining figure, seg AB is a diameter of a circle with centre O. the bisector of angleACB intersects the circle at point D. Prove that ,seg ADcongseg BD .

In the given figure, Q is the centre of the circle and PM ,PN are tangent segments to the circle. If angleMPN=50^@ find angleMQN .

In the given figure , O is the centre of the circle. If m(arc AXB)= 80^@ , then mangleAOB =

In the given figure , O is the centre of the circle. AB and AC are tangents to the circle such that BA bot CA. Prove that square BACO is a square.

In the adjoining figure circles with centres A and C touch internally at point T. Line AB is tangent to the smaller circle at point P. Point B lies on the bigger circle. Radii are 16 cm and 6 cm. Find AP.

In the adjoining figure, two circles intersect each other at points A and E. Their common secant through E intersects the circle at points B and D. The tangents of the circles at point B and D intersect each other at point C. Prove that square ABCD is cyclic.

In the adjoining figure line PA is a tangent to the circle at point A . Secant PQZ intersects chord AY in point X, such that AP = PX = XY. If PQ = 1 and QZ = 8 . Find AX.

In the adjoining figure, O is the centre of the circle. Seg AB, seg AC are tangent segments. Radius of the circle is r and l(AB) = r. Prove that , square ABOC is a square.