JAMB Mathematics 1997 Question 27

Question 27

Circle Theorems

The figure above shows circles of radii 3cm and 2cm with centre at X and Y respectively. The circles have a transverse common tangent of length 25cm. Calculate XY.

A.√630cm
B.√626cm
C.√615cm
D.√600cm

Show the answer and explanation

Answer: B (√626cm)

Explanation

Drawn as in the figure, the tangent, the difference of the radii and XY form a right-angled triangle: XY² = 25² + (3 − 2)² = 626, so XY = √626 cm.