Q. 214.5( 6 Votes )

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Answer :

Given: CA – CB

AP x BQ = AC2

To prove: ΔAPC ~ BCQ

Theorem Used:

If two corresponding sides and one angle of two triangles are equal, the triangles are said to be similar.


AP X BQ = AC2 (Given)

AP x BC = AC x AC

As AC = BC

AP x BC = AC x BC

…… (i)

Since, CA = CB (Given)

Then, CAB = CBA (Opposite angle to equal sides) …. (ii)

Now, CAB +CAP = 180° (Linear pair of angles) …… (iii)

And CBA + CBQ = 180° (Linear pair of angles) ……. (iv)

Compare equation (ii) (iii) & (iv)

CAP = CBQ …… (v)


CAP = CBQ (From equation v)

(From equation i)

Then, ΔAPC ~ ΔBCQ (By SAS similarity)

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