Answer :

Given: Area of ∆ABC = 84 cm2

PB = 8 cm


PA = 6 cm


AB = 14 cm


BQ = 8 cm (Common tangent with PB)


AR = 6 cm (Common tangent with PA)


Since QC & CR are Common tangent


Let QC = CR = x


AC = 6 + x


BC = 8 + x


So ΔROA and ΔPOA are congruent


ΔPOB and ΔQOB are congruent


ΔQOC and ΔROC are congruent


Area of ΔROA = ΔPOA = 12 cm2


Area of ΔPOB = ΔQOB = 16 cm2


Area of ΔQOC = ΔROC = 2x


The sum areas of all the small triangles = Area of ∆ABC


2 × 12 + 2 × 16 + 2 × 2x = 84


4x = 28


x = 7 cm


Answer: Length of AC = 13 cm & Length of BC = 15 cm


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