Question

Solve for t. Please include evidence. ​

Answer 1

The value of t is 5

Solution:

Given data:

AX = t, BX = 12, DX = 10 and CX = t + 6

If two chords intersect in a circle, then the product of lengths of one segment is equal to the product of lengths of other segment.

⇒ AX × BX = DX × CX

⇒ t × 12 = 10 × (t + 6)

⇒ 12t = 10t + 60

Subtract 10t from both sides of the equation, we get

⇒ 12t = 60

Divide by 12 on both sides of the equation.

⇒ t = 5

The value of t is 5.