Question

3. Is XY Tangent to circle Z?
Y
12 X
(20
Z
18

Answer 1

Answer:

XY is a tangent

Step-by-step explanation:

Given

$XY = 12$

$WY = 20$

$WZ = 8$

Required

Is XY a tangent?

XY is a tangent if:

$WY^2 = XY^2 + WX^2$

Because XY should make a right angle at point X with the circle

Where

$WX = 2 * WZ$

So, we have:

$WY^2 = XY^2 + WX^2$

$WY^2 = XY^2 + (2*WZ)^2$

$WY^2 = XY^2 + (2WZ)^2$

$WY^2 = XY^2 + 4WZ^2$

This gives:

$20^2 = 12^2 + 4*8^2$

$400 = 144 + 256$

$400 = 400$

Yes, XY is a tangent