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In the figure below, the segments WX and WY are tangent to the circle centered at 0. Given that OX=3.2 and OW-6.8, find WY.
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Answer 1

Applying the tangent to a circle theorem and the two tangents theorem, the value of WY is: 6 units.

What is the Tangent to a Circle Theorem?

The tangent to a circle theorem states that if a line is tangent to a circle, then it will be perpendicular to the radius of the circle.

What is the Two Tangents Theorem?

The two tangents theorem states that two tangents that intersect at a point outside a circle are equal in length.

Applying the tangent to a circle theorem, ΔWXO would be a right triangle. Therefore, apply Pythagorean theorem to find XW given the following:

OX=3.2

OW = 6.8

Applying the pythagroean theorem, we would have:

XW = √(OW² - OX²)

Substitute

XW = √(6.8² - 3.2²)

XW = 6

Based on the two tangents theorem, XW = WY. Therefore,

WY = 6.

In summary, applying the tangent to a circle theorem and the two tangents theorem, the value of WY is: 6 units.

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