Let J be the antipodal of A in the circumcircle of triangle ABC. Let M be...

Let J be the antipodal of A in the circumcircle of triangle ABC. Let M be the midpoint of side BC. Let H be the orthocenter of triangle ABC. Prove that H, M, and J are collinear.

Expert Solution

milcah answered 2 years ago

Let J be the antipodal of A in the circumcircle of triangle ABC. Let M be...

Let J be the antipodal of A in the circumcircle of triangle ABC. Let M be the midpoint of side BC. Let H be the orthocenter of triangle ABC. Prove that H, M, and J are collinear.

The vertices of a triangle determine a circle, called the circumcircle of the triangle. Show that...

The vertices of a triangle determine a circle, called the circumcircle of the triangle. Show that if P is any point on the circumcircle of a triangle, and X, Y, and Z are the feet of the perpendiculars from P to the sides of the triangle, then X, Y and Z are collinear.

let triangle ABC be a triangle in which all three interior angles are acute and let...

let triangle ABC be a triangle in which all three interior angles are acute and let A'B'C' be the orthic triangle. a.) Prove that the altitudes of triangle ABC are the angle bisectors of triangle A'B'C'. b.) Prove the orthocenter of triangle ABC is the incenter of traingle A'B'C'. c.) Prove that A is the A' -excenter of triangle A'B'C'.

Let ∆ABC be a triangle in R2 . Show that the centroid G is located at...

Let ∆ABC be a triangle in R2 . Show that the centroid G is located at the average position of the three vertices: G = 1/3(A + B + C).

plot each point and form the triangle ABC. Verify that the triangle ABC is a right...

plot each point and form the triangle ABC. Verify that the triangle ABC is a right triangle. Find its area. A= (-5, 10) B (2,7) C (-1,0)

triangle ABC is a right-angled triangle with the size of angle ACB equal to 74 degrees.

triangle ABC is a right-angled triangle with the size of angle ACB equal to 74 degrees. The lengths of the sides AM, MQ and QP are all equal. Find the measure of angle QPB.

Let a circle inside triangle DEF have a radius = 3, and let it be tangent...

Let a circle inside triangle DEF have a radius = 3, and let it be tangent to EF at point Z. Suppose |EZ| = 6 and |FZ| = 7. What are the lengths of d, e, and f?

In triangle ABC, cevians AD and CF are bisectors. Find area ABC / area AFD if...

In triangle ABC, cevians AD and CF are bisectors. Find area ABC / area AFD if AB = 21, AC = 28, and BC = 20.

(2) Let Vabc = [ - 5 , 5 + 5 j , - 5 j...

(2) Let Vabc = [ - 5 , 5 + 5 j , - 5 j ] T and calculate Vb012. Draw a phasor diagram illustrating the relationship Vb = Vb0 + Vb1 + Vb2 .

Prove Proposition 3.22(SSS Criterion for Congruence). Given triangle ABC and triangle DEF. If AB is congruent...

Prove Proposition 3.22(SSS Criterion for Congruence). Given triangle ABC and triangle DEF. If AB is congruent to DE, BC is congruent to EF, and AC is congruent to DF, then triangle ABC is congruent to triangle DEF. (Hint:Use three congruence axioms to reduce to the case where A=D, C=F, and points B and E are on opposite sides of line AC.)

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Let J be the antipodal of A in the circumcircle of triangle ABC. Let M be...

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Related Solutions

Let J be the antipodal of A in the circumcircle of triangle ABC. Let M be...

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