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In a cricle, two chords AB and CD inters...

In a cricle, two chords AB and CD intersect at a point P inside the circle. Prove that
`(a) Delta PAC~ Delta PDB" " (b) PA*PB=PC*PD`.

Text Solution

Verified by Experts

In `DeltaPAC and Delta PDB`, we have
`angle APC=angle DPB` [ vertically oppsite angles]
`angle PAC= angle PDB` [ angles in the same segment]
`:. Delta PAC~ Delta PDB` [ by AA-similarity]
And so, `(PA)/(PD)=(PC)/(PB) rArr PA* PB=PC*PD`.
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