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?


1 unit

1Two-thirds units

2One-half units

3 units

Answer 1

Answer:

(D)3 units

Step-by-step explanation:

To find the value of a, we use the Theorem of Intersecting Secants.

Applying this to the diagram, we have:

UV X TV = RV X SV

12 X a=(5+4)*4

12a=9*4

12a=36

Divide both sides by 12

a=3 units.

The correct option is D.

Answer 2

By applying the Theorem of Intersecting Secants, the length of TV (a) is equal to: D. 3 units.

What is the Theorem of Intersecting Secants?

The Theorem of Intersecting Secants states that the product of a secant and its external secant is equal to the product of the other secant and its external secant, when two (2) secants are drawn to a circle from an exterior (outside) point:

How to determine the length of TV?

In order to determine the length of TV (a), we would apply the Theorem of Intersecting Secants as follows:

UV × TV = RV × SV

12 × TV = (5 + 4) × 4

12TV = 9 × 4

12TV = 36

TV = 36/12

TV = 3 units.

Read more on Intersecting Secants here: https://brainly.com/question/1626547

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