Answer :

Since, AP and AR are tangents to the circle from the same point, by the property of circles they are equal. That is AP = AR.

AP = 4 cm [given]

Then AR = 4 cm [∵, AP = AR]

Also, RC = AC – AR

⇒ RC = 11 – 4 = 7 cm [∵, AC = 11 cm and AR = 4cm]

Now, we have PB = 3 cm (given) and RC = 7 cm.

Also, PB = BQ = 3 cm and RC = CQ = 7 cm [∵, PB and BQ are tangents ⇒ PB = BQ and RC and CQ are tangents ⇒ RC = CQ]

BC = BQ + CQ

⇒ BC = 3 + 7 = 10 cm

Hence, the length of BC is 10 cm.

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