Q. 94.8( 4 Votes )

# In Fig. 3, the ra

Answer :

Given: Area of ∆ABC = 84 cm^{2}

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 cm^{2}

Area of ΔPOB = ΔQOB = 16 cm^{2}

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

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Related Videos

Glimpses of India39 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation