Question

CB is tangent to ⊙A at point C. Find the radius.

Circle A is shown. Line segment A C is a radii. Line segment B C is a tangent and it intersects with the circle at point C. A line is drawn from point B to point A and a point is drawn where the line intersects with the circle. The length of the radius is r, the length of C B is 8, and the length of B to the circle is 5.

Answer 1

39/10

Explanation:

right on edg

Answer 2

The length of the radius is 3.9 units

Explanation:

From the details of the circle given, the circle is constructed with MS Visio and attached here;

From the drawing, we have;

The legs of the right triangle ABC = AC and CB

The given length of the leg CB = 8 units

The length from B to the circle on the hypotenuse side = 5 units

The length of the radius, AB = r

By Pythagoras's theorem, we have;

AB² = AB² + CB²

AB = r + 5 By segment addition postulate

Therefore;

(r + 5)² = r² + 8²

∴ (r + 5)² - (r² + 8²) = 0

r² + 10·r + 25 - r² - 8² = 0

10·r - 39 = 0

r = 39/10 = 3.9

The radius, r = 3.9 units long.