Solve the following question from the chapter circles.
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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.
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