Question

UV and RV are secant segments that intersect at point V.

Circle C is shown. Secants U V and R V intersect at point V outside of the circle. Secant U V intersects the circle at point T, and secant R V intersects the circle at point S. The length of U V is 12, the length of T V is a, the length of R S is 5, and the length of S V is 4.


What is the length of TV?

Answer 1

The answer to this question is 3

Explanation:

Answer 2

a=3

Explanation:

Intersecting Secants Theorem

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Applying the theorem of Intersecting Secants in the diagram

`TV\cdot UV=SV\cdot RV`

`a*12=4X9\\12a=36\\a=36/12\\a=3`

Therefore, the value of a=3