Two chords AB and CD of a circle interest each other at the point P(when produced) outside the circle. Prove that
triangle PAC is similar to triangle PDB.
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Two chords AB and CD of a circle interest each other at the point P(when produced) outside the circle. Prove that
triangle PAC is similar to triangle PDB.
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Ans. (i) In the triangles PAC and PDB,
APC = DPB [Common]
CAP = BDP [BAC = PAC and PDB = CDB]
= BAC = = PAC]
By AA-criterion of similarity,
APC DPB
(ii) Since APC DPB
PA.PB = PC.PD