∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).

The isosceles triangle ABC is inscribed in a circle with centre at O. If AP is a diameter of the circle. Then prove that AP is the bisetors of angle BPC .

ABCD is a quadrilateral inscribed in a circle with centre O. If angleCOD = 120^@ and angleBAC = 30^@ , then BCD is____

The isosceles triangle ABC is inscribed in the circle with centre at O.If AP be a diamtere passing through A, then show that AP is internal bisector of angle BPC .

Delta ABC is inscirbed in a circle, the bisector of the angles angle BAC, angle ABC and angle ACB intersect at the point X,Y,Zon the circle repectively. Prove that in Delta XYZ , angle YXZ=90^(@)-(1)/(2) angle BAC

AB is a diameter of a circle with centre O and AC is a chord . The straight line through O parallel to AC meets the arc BC at D. Prove that, BD= CD.

P and Q are two points ona circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the points S. If anglePSQ =20^@ , then anglePRQ =

A square is inscribed in circle of radius R, a circle is inscribed in the square, a new square in the circle and so on for n times. Find sum of the areas of all squares as n tends to infinity

The triangle ABCis inscribed in a circle, AX, BY and CZ of the angles angle BAC, angle ABC and angle ACB , intersect at the point X,Y,Z on the circle respectively. Prove that AX is perpendicular to XZ.

AB and CD are respectively arcs to two concentric circles of radii 21cm and 7cm with centre O ( See figure), If /_AOB=30^(@) , find the area of the shaded region. (usepi=(22)/(7))