#### Question

The figure shows two circles which intersect at A and B. The centre of the smaller circle is O

and lies on the circumference of the larger circle. Given ∠APB = a°.

Calculate, in terms of a°, the value of:

(i) obtuse ∠AOB,

(ii) ∠ACB

(iii) ∠ADB.

Give reasons for your answers clearly.

#### Solution

(i) obtuse ∠AOB = 2°∠APB = 2a°

(Angle at the centre is double the angle at the circumference subtended by the same chord)

(ii) OABC is a cyclic quadrilateral

∠AOB + ∠ACB = 180°

(Pair of opposite angles in a cyclic quadrilateral are supplementary)

⇒ ∠ACB = 180° - 2a°

(iii) Join AB.

∠ADB = ∠ACB =180° - 2a°

(Angle subtended by the same arc on the circle are equal)

Is there an error in this question or solution?

Solution The Figure Shows Two Circles Which Intersect at a and B. the Centre of the Smaller Circle is O and Lies on the Circumference of the Larger Circle. Given ∠Apb = A°. Calculate, in Terms of A°, the Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.