Question

Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale.

The figure consists of a chord, a secant, and a tangent to the circle. Round to the nearest hundredth, if necessary.

Answer 1

9.93

Explanation:

Secant-Tangent theorem tells us that the product of the secant segment with its external segment is equal to the square of the tangent segment.

From the diagram, we can say (let the unknown part of secant line, the part left of the segment length 5, be y):

(15+y)(10) = 17^2

Solving for y we get:

`(15+y)(10) = 17^2\\150+10y=289\\10y=289-150\\10y=139\\y=13.9`

Now we can use the chord theorem to solve for x. Chord theorem tells us that when 2 intersecting chords create 4 segments, the product of the individual chord segments are equal. Thus we can say:

5 * 13.9 = 7 * x

Now solving, we get:

`5 * 13.9 = 7 * x\\69.5=7x\\x=(69.5)/(7)\\x=9.93`

Thus x = 9.93

last answer choice is right.