Prove that the circle drawn with any side of a rhombus as a diameter, passes through the point of intersection of its diagonals.

If circles are drawn taking two sides of a triangle as diameters, prove that the point of intersection of these circles lie on the third side

P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.

If circles are drawn taking two sides of a triangle as diameters, prove that the point ofintersection of these circles lie on the third side

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

Prove that the centre of the circle circumscribing the cyclic rectangle A B C D is the point of intersection of its diagonals.

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base. Given: A triangle A B C in which A B=A C and a circle is drawn by taking A B as diameter which intersects the side B C of triangle at D . To Prove: B D=D C Construction : Join A D .

If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.