Question

Given circle E with diameter CD and radius EA. AB is tangent to E at A. if CD=28 solve for AD. round your answer to the nearest tenth of necessary

Answer 1

To find the length of AD, use the Pythagorean theorem with the radius of the circle and the diameter. Solve for AD by substituting the given values and solving the equation.

Step-by-step explanation:

To solve for AD, we need to use the properties of a tangent line to a circle. Since AB is tangent to circle E at A, it is perpendicular to the radius EA. This means that triangle EAB is a right triangle. Since CD is the diameter of the circle, we can use the Pythagorean theorem to find the length of AD:

EA² + AD² = ED²

Since EA is the radius of the circle, which is half of CD, we have:

(CD/2)² + AD² = CD²

Substituting the given value CD = 28, we can solve for AD:

(28/2)² + AD² = 28²

14² + AD² = 28²

196 + AD² = 784

AD² = 588

AD ≈ √588 ≈ 24.2