AB is a diameter of a circle with centre O. Chord CD is equal to radius OC. AC and BD produced intersect at P. Prove that : `angleAPB= 60^(@)`

AB is a diameter of the circle with centre O and chord CD is equal to radius OC (fig). AC and BD proudced meet at P. Prove that angle CPD=60^(@) .

A B is a diameter of a circle C(O ,\ r)dot Chord C D is equal to radius O Cdot If A C\ a n d\ B D when produced intersect at P , prove that /_A P B is constant.

In the adjoinig figure, AB is a diameter of the circle, CD is a chord equal to the radius of the circle. AC and BD when extended intersect at a point E. Prove that angleAEB=60^@ .

ABCD is a cyclic quadrilateral of a circle with centre O such that AB is a diameter of this circle and the length of the chord CD is equal to the radius of the circle. If AD and BC produced meet at P, show that APB = 60^(@) .

In Figure, AB is a diameter of the circle, CD is a chord equal to the radius of the circle. AC and BD when extended intersect at a point E. Prove that /_A E B = 60^@

In the adjoining figure,AB is the diameter of the circle of centre O & the chord CD is equal to radius. If P is an external point, then find the value of angleAPB .

AB and CD are two chords of a circle intersecting at P. Prove that APxxPB=CPxxPD

If AB is chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in figure. Prove that angleBAT=angleACB.

In the given figure AB is the diameter of a circle with centre O . If chord AC = chord AD, prove that : (i) are BC= are DB (ii) AB is bisector of angle CAD . Further, if the length of are AC is twice the length of are BC , find : (i) angle BAC (ii) angle ABC

In the adjoining figure, common tangents AB and CD to two circles intersect at P. Prove that AB=CD.