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In the Figure Given Below, O is the Centre of the Circle and Sp is a Tangent. If ∠Srt = 65°, Find the Value of X, Y and Z. - ICSE Class 10 - Mathematics

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Question

In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°,
find the value of x, y and z.

Solution

In the given figure, TS ⊥ SP,

m∠TSR = m∠OSP = 90°

In `triangle TSR, m angleTSR + m angleTSR + m angle RTS = 180^@`

`=> 90^@ + 65^@ + x = 180^@`

`=> x = 180^@ - 90^@ - 65^@`

`=> x= 25^@`

Now, y = 2x [Angle subtended at the centre is double that of the angle subtended by the arc at the same centre]

`=> y = 2 xx 25^@`

`:. y = 50^@`

In `triangle OSP ,m angleOSP + m angle SPO + m angle POS    =180^@`

`=> 90^@ + z + 50^@ = 180^@`

`=> z = 180^@ - 140^@`

`:. z=40^@`

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 3.3 | 4.00 marks
Solution In the Figure Given Below, O is the Centre of the Circle and Sp is a Tangent. If ∠Srt = 65°, Find the Value of X, Y and Z. Concept: Construction of Tangents to a Circle.
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