Question

Secant TQ and tangent TR intersect at point T. Chord SR and chord PQ intersect at point V. Find the values of x and y. If necessary, round to the nearest tenth.

Answer 1

x=4, y=9.6

Explanation:

Using Theorem of Intersecting Secant and Tangent

`TP X TQ=TR^2`

`9(9+12+x)=15^2\\9(21+x)=225\\189+9x=225\\9x=225-189\\9x=36\\x=4`

Next, we apply Theorem of Intersecting Chords

SV X VR=PV X VQ

5 X y = x X 12

Recall: x=4

5y=4 X 12

5y=48

y=48/5=9.6

Therefore: x=4, y=9.6