Question

A triangle has sides of length 5, 12, 13. What is the distance from the center of in-circle to the vertex of the triangle which is farthest from this center?

1. \sqrt[30]
2. 2\sqrt[30]
3. \sqrt[26]
4. 2\sqrt[26]

Answer 1

Answer:

2 is your ans bro okkkkkkkkk

Answer 2

The distance from the center of in-circle to the vertex of the triangle which is farthest from this center is  $2\sqrt{26\\}$

• The lengths of the sides are given as 5,12 and 13. Now we can see that the sides of the triangle follows pythagorean theorem as $5^{2} +12^{2} =13^{2}$
• So the triangle is right angled triangle.
• Now the inradius ,r = $\frac{5+12-13}{2}$ = 2
• Now let the vertices are A,B and C ad the incentre is I. So AI = r/sin(A/2)
• Now putting the values of r and calculating A/2 from trigonometry we get AI = 2$\sqrt{26\\}$