Question

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

Answer 1

XY is a tangent

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