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Find x in the given figure. (The vertical chord is a diameter.)

Find x in the given figure. (The vertical chord is a diameter.)-example-1
User Forshank
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Explanation:

Let the center of the circle be point O.

A right-angled triangle can be drawn using one side of chord X as the base and its height up to point O.

The height of the triangle will be 4 - 2 = 2, and the hypotenuse is the radius of the circle, which is 4.

By Pythagoras' Theorem, 2^2 + (X/2)^2 = 4^2.

So (X/2)^2 = 14, and X = 2√14.

User Martha
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