AB is a diameter and AC is a chord of a circle with centre O such that `angleBAC=30^@`. The tangent at C intersects AB at a point D. Prove that BC=BD.

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

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

In the given figure AB and CD bisect each other at O. Prove that AC = BD.

In figure, bar(AB) is a diameter of the circle, bar(CD) is a chord equal to the radius of the circle. bar(AC) and bar(BD) when extended intersect at a point E. Prove that angle AEB = 6^@ .

AB is a chord of a circle with centre o and diameter 20 cm. If AB = 12 cm, find the distance of AB from O.

In triangle ABC, AB gt AC and D is any point of BC. Prove that, AB gt AD.

In the adjacent figure, AB is a chord of circle with centre O. CD is the diameter perpendicualr to AB. Show that AD = BD

Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

In the given figure, two chords AB and CD intersect each other at the point P. Prove that AP*PB= CP*DP