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Mathematics

In the given figure, triangle ABC is circumscribed by the given circle. Use the given information to find the value of x.

In the given figure, triangle ABC is circumscribed by the given circle. Use the given information to find the value of x. Model Paper 4, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

We know that,

Tangents drawn to a circle from an external point have equal lengths.

AQ = AP = 8 cm

BR = BP = 12 cm

CR = QC

From figure,

QC = AC - AQ = 24 - 8 = 16 cm.

∴ CR = 16 cm

From figure,

BC = BR + CR = 12 + 16 = 28 cm.

Hence, x = 28 cm.

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