Question

Consider the diagram below where CD and BC are tangent to circle A. CD = 18 cm and CE = 8 cm. What is the length of the radius of circle

Answer 1

Answer:

The length of the radius of circle is 16.25 cm

Step-by-step explanation:

we know that

If CD is tangent to circle A at point D

then

the segment CD is perpendicular to the radius AD

and

ACD is a right triangle

so

Applying the Pythagorean Theorem

$AC^2=AD^2+CD^2$

we have

$AC=AE+CE=(r+8)\ cm\\AD=r\ cm\\CD=18\ cm$

substitute

$(r+8)^2=r^2+18^2$

solve for r

$r^2+16r+64=r^2+324\\16r=324-64\\16r=260\\r=16.25\ cm$