2. in the accompanying figure, $ \overrightarrow{ad} $ is tangent to circle $ o $ at $ d $ and $ \overline{abc} $ is a secant. if $ ad = 4 $ and $ ac = 8 $, find $ ab $.
4. in the accompanying diagram of circle $ o $, chords $ \overline{ab} $ and $ \overline{cd} $ intersect at point $ e $. if $ ae = 2 $, $ cd = 9 $, and $ ce = 4 $, find $ be $.
5. two secants, $ \overline{abc} $ and $ \overline{ade} $, are drawn to a circle from external point $ a $. if $ ab = 4 $, $ bc = 6 $, and $ ad = 5 $, find $ de $.

Question

Accepted Answer

# Explanation:
## Step1: Use the Chord - Chord Power Theorem
The Chord - Chord Power Theorem states that if two chords $AB$ and $CD$ intersect at a point $E$ inside a circle, then $AE\times BE=CE\times DE$.
We know that $CD = 9$ and $CE = 4$, so $DE=CD - CE=9 - 4 = 5$. Also, $AE = 2$.
## Step2: Substitute values into the formula
Substitute $AE = 2$, $CE = 4$, and $DE = 5$ into the formula $AE\times BE=CE\times DE$. We get $2\times BE=4\times5$.
## Step3: Solve for $BE$
First, simplify the right - hand side of the equation: $4\times5 = 20$. Then, solve the equation $2\times BE=20$ for $BE$. Divide both sides of the equation by 2: $BE=\frac{20}{2}$.

# Answer:
$BE = 10$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Use the Chord - Chord Power Theorem

Step2: Substitute values into the formula

Step3: Solve for \(BE\)

Answer: