AB is a diameter and AC is a chord of a circle

Question:

AB is a diameter and AC is a chord of a circle with centre 0 such that ∠BAC = 30°. The tangent at C intersects extended AB at a point D. Prove that BC

= BD.

Solution:

A circle is drawn with centre O and AB is a diameter.

AC is a chord such that ∠BAC = 30°.

Given AB is a diameter and AC is a chord of circle with certre O, ∠BAC = 30°.

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