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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.
Solution
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
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