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 = ?
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