Question

the side ab ,bc,and ca of a triangle abc touch a circlewith centre o and radius r at p, q,r respectively prove that ab+cq=ac+bq.

Answer 1

Since the lengths of tangents drawn from an exterior point to a circle are equal.
∴ AP = AR ,
   BP = BQ,
   CQ = CR
Now, AB+CQ = AP+PB+CQ
                      = AR+BQ+CQ  (∵ AP=AR and PB=BQ)
                      =(AR+CR)+BQ (∵CQ=CR)
                      = AC+BQ
∴ AB+ CQ = AC+BQ
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