Question

Find the distance between the centers of the circles in the figure.

• A. 14cm
• B. 16cm
• C. 13cm
• D. 19cm

Answer 1

The correct option is C

13cm

Let’s label the diagram and draw a line segment that joins the centers of the two circles. Also draw the segment AE perpendicular the radius BC.

Since DC is tangent to both circles, DC is perpendicular to both radii: ADand BC

We can see that AECD is a rectangle, therefore EC=AD=15cm.

This means that BE=20cm−15cm=5cm.

△ABE is a right triangle with AE=12cm and BE=5cm. We can apply the Pythagorean Theorem to find the missing side, AB

$(AB{)}^2$=$(AE{)}^2$+$(BE{)}^2$

$(AB{)}^2$=$(12{)}^2$+$(5{)}^2$

AB=13cm.