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dolphi86 [110]
3 years ago
15

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

Mathematics
1 answer:
Ratling [72]3 years ago
4 0

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

<em>Yes, XY is a tangent</em>

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