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Question
In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB||CD and AB = 10 cm then CD = ?
(a) 5 cm
(b) 12.5 cm
(c) 15 cm
(d) 10 cm
In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB||CD and AB = 10 cm then CD = ?
(a) 5 cm
(b) 12.5 cm
(c) 15 cm
(d) 10 cm
Open in App
Solution
(d) 10 cm
Draw OE ⊥ AB and OF ⊥ CD.
In Δ OEB and ΔOFC, we have:
OB = OC (Radius of a circle)
∠BOE = ∠COF (Vertically opposite angles)
∠OEB = ∠OFC (90° each)
∴ ΔOEB ≅ ΔOFC (By AAS congruency rule)
∴ OE = OF
Chords equidistant from the centre are equal.
∴ CD = AB = 10 cm
Draw OE ⊥ AB and OF ⊥ CD.
In Δ OEB and ΔOFC, we have:
OB = OC (Radius of a circle)
∠BOE = ∠COF (Vertically opposite angles)
∠OEB = ∠OFC (90° each)
∴ ΔOEB ≅ ΔOFC (By AAS congruency rule)
∴ OE = OF
Chords equidistant from the centre are equal.
∴ CD = AB = 10 cm
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