Question

10] In the figure AABC is circumscribed touching the circle at P,Q and R. If AP = 4 cm, BP = 6 cm and AC = 12 cm, find the
length of BC.

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Answer 1

Answer:

14cm

AP=AR (TANGENT DRAWN FROM OUTSIDE OF A CIRCLE)

THUS AR =4

SINCE AC=12 THEREFORE RC=AC-AR=12-4=8

RC=QC=8 (TANGENT DRAWN FROM OUTSIDE OF A CIRCLE)

BP=BQ=6 (TANGENT DRAWN FROM OUTSIDE OF A CIRCLE)

THUS BC = BQ+QC=6+8=14

Answer 2

Given,

∆ ABC is circumscribed touching the circle at P, Q and R.

AP = 4 cm

BP = 6 cm

AC = 12 cm

To find,

The length of BC.

Solution,

The length of BC will be 14 cm.

We can easily solve this problem by following the given steps.

According to the question,

∆ ABC is circumscribed touching the circle at P, Q and R.

AP = 4 cm

BP = 6 cm

AC = 12 cm

We know that the tangents drawn from the same external point are of the same length.

So,

AP = AR = 4 cm

BP = BQ = 6 cm

AC = AR+RC

12 = 4+RC

(4+RC) = 12 cm

RC = (12-4) cm (Moving 4 from the left-hand side to the right-hand side result in the change of the sign from plus to minus.)

RC = 8 cm

Now,

RC = QC = 8 cm

The length of BC = BQ+QC

BC = (6+8) cm

BC = 14 cm

Hence, the length of BC is 14 cm.