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In Figure two chords AB and CD of a cir...

In Figure two chords `AB` and `CD` of a circle intersect each other at the point P (when produced) outside the circle. Prove that
(i) `DeltaP A C~ DeltaP D B`
(ii) `P A * P B` `=` `P C * P D`

Text Solution

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(i) In `△PAC` and `△PDB`, `∠BAC=180^@−∠PAC` (linear pairs)
`∠PDB=∠CDB=180−∠BAC`
`=180^@−(180^@−∠PAC)= ∠PAC`
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