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Theorem of Geometric Mean

4. If inΔ ABC...

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4. If inΔ ABC r1=r2+r3+r then prove that triangle is right angle triangle

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Q. If in a triangle

r_{1} = r_{2} + r_{3} + r,

prove that the triangle is right angled.

Q. Prove that :

a (r r_{1} + r_{2} r_{3}) = b (r r_{2} + r_{3} r_{1}) = c (r r_{3} + r_{1} r_{2})

r

is inradius and

r_{1}, r_{2}, r_{3}

are exradius of triangle

A B C

a, b, c

are the corresponding sides.

In $△ A B C$ if $r_{1} = r_{2} + r_{3} + r$ . Then the triangle is

In acute angled triangle $A B C, r + r_{1} = r_{2} + r_{3}$ and $∠ B > \frac{π}{3}$ then

r_{1} < r_{2} < r_{3}

are the ex-radii of a right angled triangle and

r_{1} = 1, r_{2} = 2

r_{3} = . . . .

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