Given AD = 24. Find the value of x and the length of each chord. If necessary, round your answers to the nearest hundredth.

Question

asked Apr 15, 2021 76.0k views

1 Answer

Dwayne Towell · Answer 1 · 2021-04-20T07:10:19+0000

Answer:

$x\approx5.68\\\\CB\approx24.68$

Explanation:

-The product of the segments of two chords intersecting each other in a circle is always equal:

A.B=C.D

-Given the chords AD and CB, we substitute to solve for x:

$CE* EB=AE * ED\\\\\therefore x* 19=6*(24-6)\\\\19x=108\\\\x=5.6842\approx5.68$

#Length CB is the sum of segment x and segment EB:

$CB=x+EB\\\\=19+5.68\\\\=24.68$

Hence, x is approximately 5.68 and CB is 24.68