Question

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Answer 1

No.

Explanation:

Line XY will be tangent to Circle W when XY is perpendicular to the radius XW. We can test if it is perpendicular by using Pythagoras theorem as it only works on right angled triangle. If the angle WXY is 90 degrees (XY ⊥ WX) then the theorem should work.

`(XY)^2=(WX)^2+(XY)^2\\R.H.S = 66^2+54^2 = 7272\\L.H.S = 87^2 = 7569\\R.H.S \\eq L.H.S`

Thus the angle is not 90 degrees since the Pythagoras theorem doesn't work thus the line is not tangent since it is not at 90 degrees with the radius WX.

Answer 2

not a tangent

Explanation:

if XY is a tangent to the circle then ∠ WXY = 90°

using converse of Pythagoras' identity.

if the square of the longest side is equal to the sum of the squares on the other 2 sides , then the triangle is right.

longest side is WY

WY² = 87² = 7569

WX² + XY² = 66² + 54² = 4356 + 2916 = 7272

since WY² ≠ WX² + XY² , then Δ WXY is not right

then XY is not a tangent to the circle