Question

ABCD is a cyclic quadrilateral in a circle with centre O. If ∠ADC = 130°; find ∠BAC.

In the given figure, ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C, D. If ∠ADC =130°, find ∠BAC.

Answer 1

Here ∠ACB = 90°

(An angle in a semicircle is right angle.)

Also, ∠ABC = 180° – ∠ADC = 180° – 130° = 50°

(A pair of opposite angles in a cyclic quadrilateral are supplementary.)

By angle sum property of right triangle ACB,

∠BAC = 90° – ∠ABC = 90° – 50° = 40°