We are given two chords of a circle intersecting at C point.
According to intersection rule of chords of a circle
AC × CV = WC × CU
Plugging values of TC, CV, WC and UC in formula, we get
14(2x+2) = 12 (2x+5)
28x + 28 = 24x + 60.
Subtracting 28 from both sides, we get
28x + 28-28 = 24x + 60-28.
28x = 24x + 32.
Subtracting 24x from both sides, we get
28x-24x = 24x-24x + 32.
4x = 32.
Dividing both sides by 4, we get
x = 8.
We need to find the length of TV.
TV = 14+ 2x+2.
Plugging x=8, we get
TV = 14 + 2(8) +2 = 14 +16 +2 =32.
Therefore, TV = 32 units.
