Multiple choice

A circle is drawn In ∆ABC, such that it touches sides AB, BC and AC at the points P,Q and R respectively. If side AB is 4 cm more than side BC, and side AB is 2 cm more than side AC , and the perimeter of ∆ABC=32 cm, then,find the value of BP+RA?

  1. 12 cm

  2. 13 cm

  3. 33/5 cm

  4. 38/3 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let BC = x. Then AB = x + 4 and AC = x + 2. Perimeter: x + (x+4) + (x+2) = 32, giving 3x = 26, so x = 26/3 = BC. By equal tangents: BP = BQ, RA = RC, and CP = CQ. BP + RA = BQ + RC. From tangency: BQ + CP = BC and CP + CR = AC. After calculation: BP + RA = 38/3 cm.

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