A circle is inscribed in a △ABC, touching BC,CA, and AB at points P,Q, and R respectively. If AB=14 cm,AQ=11 cm and CQ=9 cm then find the length of BC.
Answer:
12 cm
- We know that the lengths of tangents drawn from an external point to a circle are equal.
Thus, AR=AQ=11 cmBP=BR and CP=CQ=9 cm - We see that BR=AB−AR=14 cm−11 cm=3 cm.
Thus, BP=BR=3 cm. - Therefore, BC=BP+CP=3 cm+9 cm=12 cm.