Question

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

Answer 1

Join AB.

In right ΔADB,

AB² = AD² + DB²

5² = AD² + 4²

AD² = 25 – 16

AD² = 9

AD = 3

Chords AE and CB intersect each other at D inside the circle

AD × DE = BD × DC

3 × DE = 4 × 9

DE = 12 cm