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JAMB Mathematics 2022 Paper

Question : 31

Total: 39

In the diagram above, XY = 8cm and OX = 5cm. Find Oz

Solution:

Concept:

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

Explanation:

From the diagram,

OZ

is perpendicular to chord

XY

, so

Z

is the midpoint of

XY

Since

XY = 8 \, \text{cm}

, we have:

XZ = \frac{XY}{2} = \frac{8}{2} = 4 \, \text{cm}

In right-angled triangle

OXZ

, the hypotenuse is

OX = 5 \, \text{cm}

and one leg is

XZ = 4 \, \text{cm}

Using Pythagoras' theorem:

OX^2 = OZ^2 + XZ^2

5^2 = OZ^2 + 4^2

25 = OZ^2 + 16

OZ^2 = 25 - 16 = 9

OZ = \sqrt{9} = 3 \, \text{cm}

Answer:

OZ = 3 \, \text{cm}

, so the correct option is D.

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