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If r1=r2+r3+r prove that the triangle is...

If `r_1=r_2+r_3+r` prove that the triangle is right angled .

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To prove that the triangle is right-angled given the condition \( r_1 = r_2 + r_3 + r \), we will follow these steps: ### Step 1: Define the triangle and its elements Let triangle \( ABC \) have sides \( a, b, c \) opposite to vertices \( A, B, C \) respectively. The semi-perimeter \( s \) of the triangle is given by: \[ s = \frac{a + b + c}{2} \] where \( r_1, r_2, r_3 \) are the inradii opposite to vertices \( A, B, C \) respectively, and \( r \) is the radius of the incircle. ...
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