find x for the question
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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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