Home
Class 12
MATHS
If in a triangle r1=r2+r3+r , prove that...

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

Text Solution

Verified by Experts

The correct Answer is:
`angle A =90^(@)`
Promotional Banner

Similar Questions

Explore conceptually related problems

In any triangle. if(a^2-b^2)/(a^2+b^2)=("sin"(A-B))/("sin"(A+B)) , then prove that the triangle is either right angled or isosceles.

In a right angles triangle, prove that r+2R=s.

In a triangle, if r_(1) gt r_(2) gt r_(3), then show a gtb gt c.

If in a triangle of base 'a', the ratio of the other two sides is r ( <1).Show that the altitude of the triangle is less than or equal to (ar)/(1-r^2)

In a triangle ABC I_1, I_2,I_3 are excentre of triangle then show that II_(1). II_(2). II_(3)=16R^(2)r.

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR are of equal area. The coordinates of R are

triangle ABC and triangle DBC are isosceles triangles on the same base BC. Prove that line AD bisects BC at right angles

Statement I In a Delta ABC, if a lt b lt c and ri si inradius and r_(1), r_(2) ,r_(3) are the exradii opposite to angle A,B,C respectively, then r lt r_(1) lt r_(2) lt r_(3). Statement II For, DeltaABC r_(1)r_(2)+r_(2)r_(3)+r_(3)r_(1)=(r_(1)r_(2)r_(3))/(r)

If a, b, c are the side of a right triangle where c is the hypotenuse, prove that the radius of the circle which touches all the side of the triangle is given by r= (a+b-c)/2 .

If the angles of a triangle are 30^(@) and 45^(@), and the included sise is (sqrt3+ 1) cm, then prove that the area of the triangle is 1/2 (sqrt3+1).