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.
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 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 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'.
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 to EF at point Z. Suppose |EZ| = 6 and |FZ| = 7. What
are the lengths of d, e, and f?
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.)