Question

Suppose that the incircle of triangle ABC touches AB at Z, BC at X, and AC at Y . Show that AX, BY , and CZ are concurrent.

Answer #1

A set of **lines** or curves are said to be
concurrent if they all intersect. at the same point. In the figure
below, the three**lines** are concurrent because they
all intersect at a single point P. The point P is called the "point
of concurrency".

BC can be shown perpendicular to AX and so on Therefore solve for altitude Let A(x1,y1) B(x2,y2) and C(x3,y3) be the vertices of the triangle ABC. If m1 is the slope of AB, then we use the two point formula to find the slope of the line m1.

Consider the triangle ABC. Suppose that the perpendicular
bisectors of line segments AB and BC intersect at point X. Prove
that X is on the perpendicular bisector of line segment AC.

If in triangle ABC and Triangle XYZ we have AB = XY, AC = XZ,
but m<A > m<X, then BC > YZ. Conversely, if BC > YZ
then m<A > m<X.

We have a triangle ABC. a=|BC|, b=|CA|, c=|AB| and ∠A=v , ∠B=r ,
and ∠C=z
Calculate c, if we know that ∠C is acute and a=8, b=3 and sin (z) =
1/7

ABC is a right-angled triangle with right angle at A, and AB
> AC. Let D be the midpoint of the side BC, and let L be the
bisector of the right angle at A. Draw a perpendicular line to BC
at D, which meets the line L at point E. Prove that
(a) AD=DE; and
(b) ∠DAE=1/2(∠C−∠B)
Hint: Draw a line from A perpendicular to BC, which meets BC in
the point F

In an isosceles triangle ABC ,AB=BC,angle B=20 . M and N are on
AB and BC respectively such that angle MCA =60, angle NAC =50.find
angle MNC

Suppose △ABC and △A'B'C' are triangles such that line AB || to
line A'B', line BC || to line B'C', and line AC || to line A'C'.
Prove that △ABC ~ △A'B'C'.

Given △ABC, extend sides AB and AC to rays AB and AC forming
exterior angles. Let the line rA be the angle bisector ∠BAC, let
line rB be the angle bisector of the exterior angle at B, and let
line rC be the angle bisector of the exterior angle at C.
• Prove that these three rays are concurrent; that is, that they
intersect at a single point. Call this point EA
• Prove that EA is the center of...

In △ABC, AB = 15 cm, BC = 10 cm, and AC = 6 cm. Find the measure
of angle B to the nearest degree.

5. Suppose that the incenter I of ABC is on the triangle’s Euler
line. Show that the triangle is isosceles.
6. Suppose that three circles of equal radius pass through a
common point P, and denote by A, B, and C the three other points
where some two of these circles cross. Show that the unique circle
passing through A, B, and C has the same radius as the original
three circles.
7. Suppose A, B, and C are distinct...

The triangle ABC,
which is not drawn to scale, represents a roof space with a span of
12 m. The roof slopes at an angle X on one side and an angle Y on
the other, producing an angle Z at the apex.
If X = 49o
and Y = 33o, calculate the lengths of the sides of the
roof, AC and BC. Give your answers in m, to 2 decimal places.
AC length:
BC length:

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 12 minutes ago

asked 14 minutes ago

asked 29 minutes ago

asked 34 minutes ago

asked 58 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago