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# formula for orthocenter of triangle

Question:I don't know how to find the circumcenter and orthocenter of a triangle because I don't know the formulas. I was given 3 points, for example, lets say the points are (1,-2), (5,3) and (-3,5). How would I go about solving the problem? I don't need you to actually solve it for me...I would just like the formulas with the numbers I provided plugged in so I know what each variable means!

Question:The 3 vertices: A (-4, 1) B (13, 9) C (6, -2) I'm trying to find the equation of the circle with the orthocenter being the center (I don't even know what the orthocenter is, and I don't know how to find it.) I have to write an equation in the form: (x - h) + (y - k) = r So I wrote this system of equations to find the orthocenter, because A, B, and C are the same DISTANCE from the orthocenter. sqrt{(-4 - h) + (1 - k) } = sqrt{(13 - h) + (9 - k) } AND sqrt{(13 - h) + (9 - k) } = sqrt{(6 - h) + (-2 - k) } Well I don't know how to solve those, and I don't even know if that's how you find the orthocenter, so I need your help. Thanks.

Answers:____________________________________ NOTE The center of the circle that circumscribes a triangle is called the "circumcenter" of the triangle. It is the point of intersection of the perpendicular bisectors of the sides. The orthocenter of a triangle is the point of intersection of the three altitudes. It won't be the center of a circumscribed circle unless the triangle is equilateral: Because, for an equilateral triangle, the perpendicular bisectors of all three sides would also be the altitudes to all three sides so that the circumcenter would also be the orthocenter. ____________________________________________________________ TO FIND THE ORTHOCENTER: To get the coordinates of the orthocenter (where the altitudes intersect) do the following: 1) Determine the slope of line AB 2) Determine the equation of the line perpendicular to AB and passing through point C. That gives you the equation of the altitude from C. 3) Repeat the procedures in steps 1 and 2 to get the equation of the altitude from either point A or point B. 4) Solve the two altitude equations simultaneously. That will get you the point (x,y) where they intersect; which is also the orthocenter. ________________________________________________ I can't tell how the circle fits into the problem. There's not enough information provided. Relative to ABC, is the circle circumscribed, inscribed, or neither and what determines its radius if its neither? Good luck __________________________________________________

Question:I need algebraic solutions. 1) (46, 63), (36, 68), (80, 02) 2) (8, 83), (36, 67), (78, 86) 3) (5, 53), (30, 3), (30, 6) Thanks.

Answers:I need help finding the orthocenter and circumcenter for these 3 triangles.? I need ALGEBRAIC solutions. 1) (46, 63), (36, 68), (80, 02) 2) (8, 83), (36, 67), (78, 86) 3) (5, 53), (30, 3), (30, 6) CALCULATING THE ORTHOCENTRE OF A TRIANGLE (This is the 3rd request I've seen this week for "orthocentre".) I answered for another Asker by providing a process that can be followed: As you likely know, the orthocentre is the intersection point of the 3 altitudes of a triangle. Depending on the type of , the orthocentre may be either interior or exterior to the . The following steps can be used to determine the co-ordinates of the orthocentre: Let s name the three given points A, B, and C. Use the slope formula to find the slope of any two sides (let's choose AB and AC): m(AB) = (Ya Yb) (Xa Xb), and repeat for side AC m(AB) = m , and m(AC) = m Calculate the slopes of any line to AB, and to AC: 1/m , and 1/m respectively Find the equations of the corresponding altitudes, and passing through the vertices C and B respectively: for which is to AB, and passes through vertex C: y Yc = ( 1/m )(x Xc) y = ( 1/m )(x Xc) + Yc for which is to AC, and passes through vertex B: y Yb = ( 1/m )(x Xyb) y = ( 1/m )(x Xb) + Yb Solve the system of these two equations, & (I trust you have the math background to do this?), which gives the co-ordinates of the orthocentre. CALCULATING THE CIRCUMCENTRE OF A TRIANGLE The circumcentre is the intersection point of the 3 perpendicular bisectors of the sides of a triangle. Depending on the type of , the circumcentre may be either interior or exterior to the . The following steps can be used to determine the co-ordinates of the circumcentre: Let s name the three given points A, B, and C. Using the midpoint formula, calculate the midpoints, D and E, of any two sides (let's choose AB and AC) Midpoint of AB = D[( (Xa +Xb), (Ya + Yb)] Midpoint of AC = E[( (Xa +Xc), (Ya + Yc)] Use the slope formula to find the slope of those same two sides (AB and AC): m(AB) = (Ya Yb) (Xa Xb), and repeat for side AC m(AB) = m , and m(AC) = m The slopes of any line to AB, and to AC: 1/m , and 1/m respectively Find the equations of the bisectors, and passing through midpoints D and E respectively: for which is to AB, and passes through midpoint D: y Yd = ( 1/m )(x Xd) y = ( 1/m )(x Xd) + Yd for which is to AC, and passes through midpoint E: y Ye = ( 1/m )(x Xe) y = ( 1/m )(x Xe) + Ye Solve the system of these two equations, and , which gives the co-ordinates of the circumcentre If you carefully follow the procedures I have mapped out above, I am confident that you can solve the three problems for yourself. ["GIVE a person a fish (ie the answer); feed him for today. TEACH a person to fish (ie how to solve his own problems), and he can feed himself for a lifetime."] Cheers! .

Question:I only need to know how to find them on a right triangle.

Answers:The circumcenter is the point of concurrency of the perpindicular bicectors. The incenter is the point of concurrency of the angle bisectors The orthocenter is the point of concurrency of the medians Do the constructions and you can find the answers. A tip for a right triangle, the circumcenter is the midpoint on the hypotenuse