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In Fig. 6.61, two chords AB and CD intersect each other at the point P. Prove that: AP. PB equals CP DP

Q7  (2)   In Fig. 6.61, two chords AB and CD intersect each other at the point P. Prove that :
              AP . PB = CP . DP

              

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In \triangle APC\, \, and\, \triangle DPB,

\angle APC\, \, = \angle DPB        ( vertically opposite angle)

\angle CAP\, \, = \angle BDP      (Angles in the same segment)

\triangle APC\, \, \sim \triangle DPB         (By AA)

\frac{AP}{DP}=\frac{PC}{PB}=\frac{CA}{BD}             (Corresponding sides of similar triangles are proportional)

\Rightarrow \frac{AP}{DP}=\frac{PC}{PB}

\Rightarrow AP.PB=PC.DP

 

 

 

 

 

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