Mathematics
In the given figure, quadrilateral ABCD is circumscribed and AD ⟂ AB. If the radius of the incircle is 10 cm, find the value of x.
Circles
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Answer
From figure,
OS = OP (As both are radius of circle.)
Since,
Adjacent sides are equal and each angle is a right angle.
∴ AP = OS.
From A, AS and AP are the tangents to the circle.
∴ AP = AS = 10 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)
From C, CR and CQ are the tangents to the circle.
∴ CQ = CR = 27 cm. (∵ if two tangents are drawn to a circle from an external point then the tangents have equal lengths.)
From figure,
BQ = BC - CQ = 38 - 27 = 11 cm.
Now from B, BQ and BP are the tangents to the circle
BP = BQ = 11 cm.
⇒ AB = x = AP + BP = 10 + 11 = 21 cm.
Hence, x = 21 cm.
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