#### Question

In the following figure, the line ABCD is perpendicular to PQ; where P and Q are the centres of

the circles. Show that:

(i) AB = CD,

(ii) AC = BD.

#### Solution

In the circle with centre Q, QO ⊥ AD

∴ OA= OD …………… (1)

(Perpendicular drawn from the centre of a circle to a chord bisects it)

In the circle with centre P, PO ⊥ BC

∴ OB=OC ……………..(2)

(Perpendicular drawn from the centre of a circle to a chord bisects it)

(i)

(1) – (2) Gives,

AB = CD ……………(3)

(ii) Adding BC to both sides of equation (3)

AB+BC = CD+BC

⇒ AC = BD

Is there an error in this question or solution?

Solution In the Following Figure, the Line Abcd is Perpendicular to Pq; Where P and Q Are the Centres of the Circles. Show That: (I) Ab = Cd, (Ii) Ac = Bd. Concept: Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof).