Question

All three circles are tangents to the same line and also to each other. Circles C2 and C3 have equal radii. Find the radius of C2, if the radius of C1 is equal to 10 cm.

• A. 30 cm
• B. 35 cm
• C. 40 cm
• D. 45 cm

Answer 1

The correct option is C

40 cm

From the above figure,
Given: Radius of smaller circle C1 is 10 cm
To find: Radius of circle C2
Let r, R2 and R3 be the radii of circles C1, C2 and C3 respectively with R2 = R3 = $x$
Applying Pythagoras theorem to triangle C2QC1

$(QC1{)}^2+(C2Q{)}^2=(C2C1{)}^2$
$\Rightarrow x^2+(x-10{)}^2=(x+10{)}^2$
$\Rightarrow 2x^2+100-20x=x^2+100+20x$
Upon solving,
$x^2=40x$
$x=40$
Therefore, the radius of the circle C2 is 40 cm