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WAEC Mathematics 2012 Paper

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Question : 36

Total: 49

The diagram is a circle centre O. If < SPR = 2m and < SQR = n, express m in terms of n

m = $\; \frac{n}{2}$
m = 2n
m = n - 2
m = n + 2

Solution:

Concept:

Angles in the same segment of a circle standing on the same chord are equal.

Explanation:

In the given circle,

\angle SPR

and

\angle SQR

subtend the same chord

SR

.

Thus,

\angle SPR = \angle SQR

.

Given:

\angle SPR = 2m

and

\angle SQR = n

.

So,

2m = n

.

Dividing both sides by

2

, we get:

m = \frac{n}{2}

.

Answer:

Option A:

m = \frac{n}{2}

.

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