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`.

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 .

The equilateral triangle ABC is inscribed in a circle. If P is any point on the ar BC, then prove that AB=PB+PC .

Delta ABC is an acute angle triangle inscribed in a circle in a circle .AD is a diameter of the circle . Two perpendiculars BE and CF are drawn from B and C to AC and AB respectively , which intersect each other at the point G . Prove that BDCG is a parallelogram.

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

AD and AC are two equal chords of a circle with centre O. AB is the diameter of the circle. If angleCOD =140^@ , then angleOBC =

AB is a diameter of a circle with centre at O. C is any point on the circle. If angleBOC = 110^@ , then angleBAC =

A circle is inscribed in a square. If the side of the square be 10 cm, then the diameter of the circle is

Show that of all isosceles triangles inscribed in a given circle, the equilateral triangle has the greatest area.

An isosceles triangle with base 24 and legs 15 each is inscribed in a circle . Find the radius