Question

If in an isosceles triangle ABC, AC = BC and AB² = 2AC², then find the value of angle C.

Answer 1

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Answer 2

The value of angle C is  90°.

Step-by-step explanation:

Given:

$AB^2 = 2AC^2$

⇒ $AB^2 = AC^2 + AC^2$

⇒ $AB^2 = AC^2 + BC^2$    [ [∵ Given: AC = BC]]

The expression given above is equivalent to expression of Pythagoras theorem, $h^2 = p^2 + b^2$, which corresponds to a right angled triangle.

Also, h = AB and angle opposite to hypotenuse is right angle.

Thus ∠C = 90°.