Question

In circle A as pictured above, segment DC is tangent to circle A at D.

Also, DC = 24 and BC = 18.

Find the length of the radius of circle A.

A)7

B) 6√7

C)25

D)12√5

Answer 1

• AC=2(BC)=2(18)=36
• DC=34

Now

It's a right angle triangle

Perpendicular be radius and P

Apply Pythagorean theorem

$\\ \rm\rightarrowtail P^2=36^2-24^2$

$\\ \rm\rightarrowtail P^2=720$

$\\ \rm\rightarrowtail P=\sqrt{720}$

$\\ \rm\rightarrowtail P=\sqrt{2(2)(2)(2)(3)(3)(5)}$

$\\ \rm\rightarrowtail P=4(3)\sqrt{5}$

$\\ \rm\rightarrowtail P=12\sqrt{5}$