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Arc/Chord Properties of Circles

Fill In The B...

Question

Fill In The Blanks

If AOB is a diameter of a circle and C is a point on the circle, then the AC² + BC²= ____________.

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Solution

Given:
AOB is a diameter of a circle
C is a point on the circle

Since, AOB is the diameter of the circle
Therefore, ∠ACB = 90° (angle in the semi circle) ...(2)

In right angled ∆ABC,
Using pythagoras theorem.
AC² + BC² = AB²

Hence, AC² + BC²= AB².

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