If r1 = r + r2 + r3 then prove that the triangle is a right angled triangle - Maths - Introduction to Three Dimensional Geometry

Question

If r1 = r + r2 + r3 then prove that the triangle is a right angled
triangle

Brijendra Pal · Accepted Answer

Dear Student,
Dear Student,
Dear Student,
r1=r+r2+r3△s-a=△s+△s-b+△s-c1s-a-1s=1s-b+1s-cass-a= 2s-b-cs-bs-cass-a= a+b+c-b-cs-bs-c1ss-a=1s-bs-cs2-sb+c+bc= s2-assa-b-c+bc=0 a+b+c2a-b-c= -bca2-b+c2= -2bca2-b2-c2-2bc=-2bca2= b2+c2So it is a right angle triangle
Regards

If r1 = r + r2 + r3 then prove that the triangle is a right angled triangle.