Question

In the adjoining figure, the circle with center D touches the sides of ∠ACB at A and B. If ∠ACB = 52°, find the measure of ∠ADB.

Answer 1

In a figure, D is the centre of the circle.

ADBC is a quadrilateral.

∴ ∠ACB + ∠CAD + ∠CBD + ∠ADB = 360°  ......[The sum of all angles of a quadrilateral is 360°.]

∴ 52° + 90° + 90° + ∠ADB = 360°  ......[Tangent theorem]

∴ ∠ADB + 232° = 360°

∴ ∠ADB = 360° – 232°

∴ ∠ADB = 128°