ICSE Class X Math 2015 Solved Paper

Question : 12

Total: 52

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 △ OSP,‌‌∠OSR=90∘
[Radius is perpendicular to tangent]

In ∆ TSR
x+90∘+65∘=180∘
(Angle sum property of triangle)
‌∴‌‌x=25∘
‌∠SOQ=2∠STR
[Angle at centre =2× Angle at circumference]
y=2×25=50∘
In ∆ OSP,
50∘+90∘+z=180∘
(Angle sum property of triangle)
∴‌‌z=40∘

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