Two chords AB and CD of a circle intersect each other at a point E outside the circle. If AB = 11 cm, BE = 3 cm and DE = 3.5 cm, then CD = ?

Question

Philoid · Accepted Answer

Given: AB = 11cm, BE = 3cm and DE = 3.5cm

Construction: Join AC

Here,

AE: CE = DE: BE

AE×BE = DE×CE

(AB + BE)×BE = DE×(CD + DE)

(11 + 3)×3 = 3.5×(CD + 3.5)

14×3 = 3.5×(CD + 3.5)

3.5×(CD + 3.5) = 42

(CD + 3.5) = = 12

CD = 12—3.5 = 8.5

∴ CD = 8.5