Question

In the figure below, Z is the center of the circle. Suppose that OR=4, ST= 4, UZ= 6, and VZ=4x-6. Find the following.

Answer 1

Answer:

x = 3 units

SV = 2 units

Step-by-step explanation:

In$\odot Z$ QR and ST are chords such that:

QR = ST = 4

That is both the chords are equal in measure.

Equal chords are at equal distance from the center of the circle. Therefore,

VZ = UZ

4x - 6 = 6

4x = 6 + 6

4x = 12

x = 12/4

x = 3 units

Since, perpendicular dropped from the center of the circle bisects the chord.

$\therefore SV = \frac{1}{2} ST$

$\therefore SV = \frac{1}{2} \times 4$

$\therefore SV = 2\: units$