Q. 104.8( 4 Votes )

# 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. If AB = 10 cm, then CD = ?

A. 5cm

B. 12.5cm

C.15cm

D. 10cm

Answer :

Given: AB||CD and AB = 10cm

Construction: Drop perpendiculars OE and OF on to AB and CD respectively.

Now,

Consider ΔBOE and ΔCOF

Here,

OB = OC (radius)

∠OEB = ∠OFC (right angle)

∠COF = ∠BOE (vertically opposite angles)

∴ By AAS congruency ΔBOE ΔCOF

∴ OE = OF (by congruent parts of congruent triangles)

Chords equidistant from center are equal in length

That is CD = AB = 10cm

∴ CD = 10cm

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