A circle is inscribed in \(\triangle ABC\), touching AB at P, BC at Q and AC at R. If AR = 7 cm, RC = 9 cm and AB = 15 cm, what is the perimeter of \(\triangle ABC\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 48 cm
The two tangents drawn to a circle from an outside point are equal in length. Each vertex of the triangle is such a point.
From A: AP \(=\) AR \(=7\) cm
BP \(=\) AB \(-\) AP \(=15-7=8\) cm, and from B: BQ \(=\) BP \(=8\) cm
From C: CQ \(=\) CR \(=9\) cm, so BC \(=8+9=17\) cm
AC \(=7+9=16\) cm
Perimeter \(=15+17+16=48\) cm
