Question

Find the value of x in the following figure, where O is the centre of the circle: 

Answer 1

Given:

O is the centre.

AC is a diameter (it passes through O).

∠BAC = 64°.

We have to find x = ∠BDC.

Step 1: Identify the intercepted arc
Angle ∠BAC is an inscribed angle whose sides are chords BA and AC.
So it intercepts arc BC.

Therefore arc BC corresponds to inscribed angle 64°.

Step 2: Use the inscribed angle property
Any inscribed angle that subtends the same arc has the same measure.

Angle ∠BDC is also an inscribed angle, and its sides are chords DB and DC, which also intercept arc BC.

∠BAC = ∠BDC

x = 64°.