Engineering Board Exam Reviewer · Properties of Triangles · hard
A right triangle has legs 20 and 21 and hypotenuse 29. Find the distance between its incenter and circumcenter.
- 8.5
- 6.02
- 14.5
- 2.5
Answer
B. 6.02
Solution
R=29/2=14.5 and r=20+21-29/2=6. By Euler's formula, d2=R(R-2r)=14.5(2.5)=36.25, so d=6.02.
More Properties of Triangles questions
- The three altitudes of a triangle are 12, 15 and 20 units long. Find the area of the triangle.
- In triangle ABC, BC=14, CA=15 and AB=13. Find the distance from vertex A to the incenter.
- Find the area of a triangle with sides 9, 10 and 17.
- A triangle is inscribed in a circle of radius 10. Find the side opposite an angle of 30°.
- For the triangle with sides a=13, b=14 and c=15, find the exradius opposite side a.
- Find the radius of the inscribed circle of a right triangle with legs 6 and 8.
- In triangle ABC, BC=6, CA=9 and AB=10. The bisector of angle C meets AB at D. Find the length of DB.
- Find the altitude to the longest side of the triangle with sides 13, 14 and 15.
- In the triangle with sides 13, 14 and 15, find the length of the median drawn to the side of length 14.
- Find the radius of the circumscribed circle of the triangle with sides 13, 14 and 15.