Question

the side AB,BC,CA of triangle ABC touch a circle with centre O and radius r at PQR. proof (1). AB+CQ=AC+BQ (2). area of triangle abc = 1/2 perimetre of triangle * r

Answer 1

since the lengths of tangents drawn from an exterior point to a circle from equal
AP=AR
BP=BQ
CQ=CR
now,AB+CQ=AP+PB+CQ
=AR+BQ+CQ(AP=ADandAB=BQ
=AR+CR+BQ(CQ=CR)
=AC+BQ
AB+CQ=AC+BQ
hence,proved