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.

CB ⊥ AC by the radius-tangent theorem, so ∠C is a right angle.

ΔABC is a right triangle, so apply the Pythagorean theorem.

Use the steps and solve for the radius.

r2 + 82 = (r + 5)2
r2 + 64 = r2 + 10r + 25
r =

Answer 1

r=39/10

Explanation:

thats the answer on edg 2020

Answer 2

3.9 Units

Explanation:

CB ⊥ AC by the radius-tangent theorem, so ∠C is a right angle.

In ΔABC, applying the Pythagorean theorem.

`r^2 + 8^2 = (r + 5)^2\\r^2 + 64 = r^2 + 10r + 25\\64=10r + 25\\10r=64-25\\10r=39\\$Divide both sides by 10\\r=3.9 Units`

The radius of the circle is 3.9 Units