Math, asked by jaip39966, 4 months ago

find x for the question​

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Answered by judith0209
1

Answer:

x = 21cm

Step-by-step explanation:

Construction : Join OP.

Name the point where the lines P and Q intersect T.

In  quadrilateral OSAP,

∠OSA = 90°-------(tangent is perpendicular to radius at point of contact)

∠APO = 90°-------(tangent is perpendicular to radius at point of contact)

∠SAP = 90°-----(given)

∠S + ∠P + ∠A + ∠O = 360°------(angles of a quadrilateral)

90 + 90 +90 + ∠O = 360

∠O = 360 - 270

∠O = 90°

Therefore, OSAP is a rectangle/square.

∴ OS = AP-----(opposite sides of a rectangle)

∴ AP = 10cm-------(1)

Now,

CR = CQ-------(tangents from an external point are equal)

CQ = 27cm

QT = 38 - 27

QT = 11cm

PT = QT-----(tangents from an external point are equal)

PT = 11cm-----(2)

x = AP + PT

x = 10 + 11

x = 21cm

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