JAMB 1997 · UME · Q27✱✱

Circle geometry

The figure shows circles of radii $3\text{ cm}$ and $2\text{ cm}$ with centres $X$ and $Y$ respectively. The circles have a direct common tangent of length $25\text{ cm}$ . Calculate $XY$ .

Not to scale.

Worked solution (try it first)

Each radius is perpendicular to the tangent, so the two radii and the tangent form a trapezium with two right angles.
Draw a line from $Y$ parallel to the tangent to meet radius $X$ at a right angle.
It is 25 cm long and cuts off $3 - 2 = 1$ cm of that radius.
$XY$ is the hypotenuse of this right-angled triangle, so by Pythagoras $XY^2 = 25^2 + 1^2 = 626$ .
So $XY = \sqrt{626}$ cm, option B.

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