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Triangles

Question
Classify the triangle as acute, right angled, obtuse based on the given 3 sides of a triangle.

Consider an equilateral triangle with each side a. The sum of squares of first two sides is greater than the square of third side.
a2 + a2 > a2
In general if the sum of squares of shorter sides is greater than the square of the larger side the triangle is acute.
a2 + b2 > c2

For right angled triangle pythagorean theorem holds true
a2 + b2 = c2

If a2 + b2 < c2 the triangle is obtuse

Fact
In-center is a point in a triangle where the angle bisectors intersect.
It is also the center of the triangle's in-circle, the largest circle which can be fit inside the triangle.

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