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# Question 22. (a) In the figure (i) 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. (2015) (b) In the figure (ii) given below, O is the centre of the circle. PS and PT are tangents and ∠SPT = 84°. Calculate the sizes of the angles TOS and TQS.

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This is circle based question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In this question we have, O is the centre of the circle and SP is a tangent.

∠SRT = 65°, and by using these we have to find the value of x, y and z.

This question has been asked in 2015.

In the second part of the question we have O is the centre of the circle. PS and PT are tangents and ∠SPT = 84°.

Now we have to calculate the sizes of the angles TOS and TQS.

ICSE Avichal publication
Understanding ICSE Mathematics
Question no 22

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### 1 Answer

1. Solution:
Consider the following figure:
TS ⊥ SP,
∠TSR = ∠OSP = 90°
In ∆TSR,
∠TSR + ∠TRS + ∠RTS = 180°

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