ICSE Class X Math 2015 Solved Paper

Question : 32

Total: 52

AB and CD are two chords of a circle intersecting at P. Prove that AP×PB=CP× PD.

Solution:

To Prove: AP×PB=CP×PD
Construction: Join AD and CB.
Proof: In △APD and △CPB

∠A=∠C
[angles of the same segment]
∠C=∠B
[angles of the same segment]
∴△APD∼△BPC [AA Postulate]
∴‌‌‌

=‌

[corresponding sides of similar ∆s are proportional]
∴‌‌AP×PB=CP×PD

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