Question

NO LINKS!! URGENT HELP PLEASE!! Find the measure of line segment BD​

Answer 1

BD = 14

Step-by-step explanation

4(5x) = 8x5

20x=40

x=2

BD = 4 + 5(2)

BD = 14

Answer 2

`\overline{\sf BD}=14`

Explanation:

The given diagram shows a circle with two intersecting chords, with chord BD intersecting chord AC at point F.

According to the Intersecting Chords Theorem, when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

Therefore, according to the Intersecting Chords Theorem:

`\sf \overline{BF} \cdot \overline{FD}=\overline{A\:\!F} \cdot \overline{FC}`

Substitute the values of each line segment into the equation, and solve for x:

`\begin{aligned}4 \cdot 5x&=5 \cdot 8\\20x&=40\\20x / 20&=40/20\\x&=2\\\end{aligned}`

The measure of line segment BD is the sum of line segments BF and FD. Therefore, to find the measure of BD, substitute the found value of x into the sum equation:

`\begin{aligned}\sf \overline{BD}&=\sf \overline{BF}+\overline{FD}\\&=4+5x\\&=4+5(2)\\&=4+10\\&=14\end{aligned}`

Therefore, the measure of line segment BD is 14 units.