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# In the diagram, O is the centre of the circle of the circle, PR is a tangent to ...

### Question

In the diagram, O is the centre of the circle of the circle, PR is a tangent to the circle at Q, < SOQ = 86o. Calculate the value of < SQR.

A) 43o

B) 47o

C) 54o

D) 86o

### Explanation:

Construction: draw a line from Q to point P and another line from S to point P.

< SOQ = 2< QPS (< at centre is twice < on the circumference)

< QPS $$\frac{86}{2} = 43$$

< SQR = < QPS ( < between a chord and tangent = < in the alternate segment)

< SQR = 43o

## Dicussion (1)

• Construction: draw a line from Q to point P and another line from S to point P.

< SOQ = 2< QPS (< at centre is twice < on the circumference)

< QPS $$\frac{86}{2} = 43$$

< SQR = < QPS ( < between a chord and tangent = < in the alternate segment)

< SQR = 43o