Question

In the given figure, AE and BC intersect each other as point D. If ∠CDE = 90°, AB = 5 cm, BD = 4 cm and CD = 9 cm, find AE.

Answer 1

In the given circle,

Chords AE and BC intersect each other at D at right angle i.e., ∠CDE = 90°, AB is joined AB = 5 cm, BD = 4 cm, CD = 9 cm

Now we have to find AE.

Let DE = x m

Now in right ΔABD,

AB² = AD² + BD²  ...(Pythagoras Theorem)

`\implies` (5)² = AD² + (4)²

`\implies` 25 = AD² + 16

`\implies` AD² = 25 – 16 = 9 = (3)²

∴ AD = 3 cm

∵ Chords AE and BC intersect each other at D inside the circle

∴ AD × DE = BD × DC

`\implies` 3 × x = 4 × 9

`\implies x = (4 xx 9)/3 = 12  cm`

`\implies` DE = 12 cm

∴ AE = AD + DE

= 3 + 12

= 15 cm