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Circumcenter and Construction of Circumcircle in a Triangle

In an equilat...

Question

In an equilateral triangle ABC, AN ⊥ BC. Prove that AN² = 3BN².

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Solution

It is given that ΔABC is an equilateral triangle.

We know that an altitude of an equilateral triangle divides the side it intersects into two equal parts.

∴ BN = CN =

Applying Pythagoras theorem in right ΔABN, we have:

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