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WAEC Mathematics 2024 Paper

Question : 23

Total: 50

In the diagram above, O is the centre of the circle. If | $\overline{OA}$ = 25 cm and | $\overline{AB}$ = 40 cm, find | $\overline{OH}$ |

Solution:

Concept:

A perpendicular from the centre of a circle to a chord bisects the chord.

Explanation:

Since

OH

is perpendicular to chord

AB

, it divides

AB

into two equal parts.

Thus,

AH = HB = \frac{40}{2} = 20

cm.

In right-angled triangle

AOH

OA = 25

cm is the hypotenuse and

AH = 20

cm.

Using Pythagoras theorem:

(OH)^2 = (OA)^2 - (AH)^2

(OH)^2 = 25^2 - 20^2 = 625 - 400 = 225

Taking the square root:

OH = \sqrt{225} = 15

cm.

Answer:

|OH| = 15

cm.

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