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In figure (i) given below, triangle ABC is circumscribed, find x.

In figure (i) given below, triangle ABC is circumscribed, find x. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Circles

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Answer

From figure, AP and AQ are the tangents to the circle.

∴ AQ = AP = 4 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

From figure, BP and BR are the tangents to the circle.

∴ BR = BP = 6 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

From figure,

CQ = CA - AQ = 12 - 4 = 8 cm.

From figure, CQ and CR are the tangents to the circle.

∴ CR = CQ = 8 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)

From figure,

x = BR + CR = 6 + 8 = 14 cm.

Hence, the value of x = 14 cm.

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