A circle is inscribed in a ABCABC, touching BC,CA,BC,CA, and ABAB at points P,Q,P,Q, and RR respectively. If AB=14 cm,AQ=11 cmAB=14 cm,AQ=11 cm and CQ=9 cmCQ=9 cm then find the length of BCBC.
R Q P B C A


Answer:

12 cm12 cm

Step by Step Explanation:
  1. 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
  2. We see that BR=ABAR=14 cm11 cm=3 cm.
    Thus, BP=BR=3 cm.
  3. Therefore, BC=BP+CP=3 cm+9 cm=12 cm.

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