Question

1. (overleftrightarrow{ac}) is tangent to the circle below. if (ac = 10), and (cb = 4), then what is the length of (bd)?

Explanation:

Step1: Apply tangent-secant theorem

The tangent-secant theorem states that for a tangent $AC$ and a secant $CD$ (intersecting the circle at $B$ and $D$), $AC^2 = CB \times CD$. Substitute the given values:
$10^2 = 4 \times CD$

Step2: Solve for length of CD

Calculate $10^2 = 100$, then rearrange to solve for $CD$:
$CD = \frac{100}{4} = 25$

Step3: Calculate length of BD

Since $CD = CB + BD$, rearrange to solve for $BD$:
$BD = CD - CB = 25 - 4$

Answer:

21