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=√(720)`

`\\ \rm\rightarrowtail P=√(2(2)(2)(2)(3)(3)(5))`

`\\ \rm\rightarrowtail P=4(3)√(5)`

`\\ \rm\rightarrowtail P=12√(5)`