Q. 94.8( 4 Votes )

# In Fig. 3, the ra

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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