Test Index

ICSE Class X Math 2015 Paper

© examsnet.com
Question : 12 of 52
Marks: +1, -0
In the figure given below, OO is the centre of the circle and SPS P is a tangent. If ∠SRT=\angle SRT= 65∘65^{\circ}, find the value of x,yx, y and zz.
Solution:  
In △\triangle OSP,    ∠OSR=90∘\;\; \angle OSR=90^{\circ}
[Radius is perpendicular to tangent]
In â–³\triangle TSR
x+90∘+65∘=180∘x+90^{\circ}+65^{\circ}=180^{\circ}
(Angle sum property of triangle)
  ∴    x=25∘\; \therefore \;\; x=25^{\circ}
  ∠SOQ=2∠STR\; \angle SOQ=2 \angle STR
[Angle at centre =2×=2 \times Angle at circumference]
y=2×25=50∘y=2 \times 25=50^{\circ}
In â–³\triangle OSP,
50∘+90∘+z=180∘50^{\circ}+90^{\circ}+z=180^{\circ}
(Angle sum property of triangle)
∴    z=40∘\therefore \;\; z=40^{\circ}
© examsnet.com
Go to Question:
Prev Question
Next Question