Multiple choice

A circle is inscribed in a △ABC, touching AB,BC and CA at points P,Q and R respectively. If AC - AB= 4" " cm,AB=BC-7" " cm and the perimeter of △ABC is 44" " cm, then BQ+CR is equal to :

  1. 16 cm

  2. 18 cm

  3. 12 cm

  4. 15 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the tangent properties of an inscribed circle: from a point outside a circle, the two tangent segments are equal. So BP = BR, AP = PR, and CQ = CR. Solving the three equations: AC - AB = 4, AB = BC - 7, and perimeter = 44 gives AB = 11, BC = 18, AC = 15. BQ = (BC + AB - AC)/2 = 7 and CR = (AC + BC - AB)/2 = 11, so BQ + CR = 18 cm. Option B is correct.

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