The distance between the circumcentre and the orthocentre of the triangle formed by $$1$$,$$2$$,$$3$$,$$3$$,−$$1$$,$$5$$,$$4$$,$$0$$,−$$3is$$

Question

The distance between the circumcentre and the orthocentre of the triangle formed by $$1$$,$$2$$,$$3$$,$$3$$,−$$1$$,$$5$$,$$4$$,$$0$$,−$$3is$$

Infinity Learn · Accepted Answer

The given vertices $$areA1$$,$$2$$,$$3$$,$$B3$$,−$$1$$,$$5$$,$$C4$$,$$0$$,−$$3The$$ sides of the triangle are $$AB=4+9+4=17BC=1+1+64=66CA=9+4+36=49Observing$$ the sides of the triangle, the triangle is right angled triangle, because square of one side is sum of the squares of the other two sides. Since it is right angled triangle, the ortho center is vertex at right angle and the circum center is midpoint of hypotenuseThe distance between the ortho center and circum center is half of the hypotenuse Hence, the required distance is $$662$$

The distance between the circumcentre and the orthocentre of the triangle formed by $(1, 2, 3), (3, - 1, 5), (4, 0, - 3)$ is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The distance between the circumcentre and the orthocentre of the triangle formed by 1,2,3,3,−1,5,4,0,−3is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The distance between the circumcentre and the orthocentre of the triangle formed by $(1, 2, 3), (3, - 1, 5), (4, 0, - 3)$ is