Question

Secant TP and tangent TR intersect at point T Chord SR and chord PO intersect

at point V. Find the values of x and y. If necessary, round to the nearest tenth.

A

x=2

y=4

B. x= 11.6

y = 11.6

C.

X = 11.6

y = 232

D. x = 18.3

y=36.6

Answer 1

(C)x=11.6, y=23.2

Explanation:

Using Theorem of Intersecting Secant and Tangent

`TQ$ X TP=TR^2`

`10(10+x+4)=16^2\\10(14+x)=256\\140+10x=256\\10x=256-140\\10x=116\\$Divide both sides by 10\\x=11.6`

Next, we apply Theorem of Intersecting Chords

PV X VQ=SV X VR

4 X x= 2 X y

Recall: x=11.6

2y=4 X 11.6

2y=46.4

y=46.4/2=23.2

Therefore: x=11.6, y=23.2

The correct option is C