Problem

26. Determine the length of chord CD. [4 marks]

Answer

Expert–verified
Hide Steps
Answer

The final answer is \(\boxed{2\sqrt{5}}\).

Steps

Step 1 ：Let the center of the circle be O, and let the point where the radius of the circle bisects the chord be E. Thus, the line segment from the center of the circle to point E has length 2, and we have \(\triangle ODE\) with a leg of 2 and a hypotenuse of 3.

Step 2 ：Using the Pythagorean theorem, we can find the length of the other leg, DE: \(DE^2 = 3^2 - 2^2 = 5\), so \(DE = \sqrt{5}\).

Step 3 ：Since DE is \(\frac{CD}{2}\), we can find the length of chord CD: \(CD = 2 \times DE = 2 \times \sqrt{5}\).

Step 4 ：The final answer is \(\boxed{2\sqrt{5}}\).

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More