Question

AD is a common internal tangent to circles B and C. Find the length of the radius of circle B. Round to the nearest hundredth.

Answer 1

ΔABE ~ ΔDCE
AB=AE*DC/DE=18*4/6=12

Answer 2

As AD is common tangent,

<BAE=90=<CDE

Also <BEA=<CED as they are opposite angles

By AAA, the two triangles, ABE and DCE, are similar

so AB/EA = DC/ED

AB = EA * DC/ED = 18 * 4/6

= 12