JAMB 2000 · UME · Q30

Circle geometry

In the diagram, $EFGH$ is a circle with centre $O$ . $FH$ is a diameter and $GE$ is a chord which meets $FH$ at right angles at $N$ . If $NH = 8$ cm and $EG = 24$ cm, calculate $FH$ .

Worked solution (try it first)

A diameter perpendicular to a chord bisects it, so $EN = NG = 12$ cm.
Intersecting chords: $FN \times NH = EN \times NG$ , so $8 \times FN = 12 \times 12 = 144$ and $FN = 18$ cm.
So $FH$ is $FN + NH = 18 + 8 = 26$ cm, option C.

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