jugoslav

An incenter is a point in a triangle where all 3 angle bisectors intersect.

So, the answer is a.

We know that the ratio of midsegment WX to side TV is 1 : 2

So, we have     2 * WX = TV

                         2(23 - 2x) = 64 - 10x

                         x = 9/4

                        TV = 64 - 10(9/4) = 83/2

12 / 9 = 32 / EH          EH = 24      ==>  EH = UV

UV / VT = UE / EH                 24 / VT = 32 / 24

VT = 18

When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1/2(257 - 103) = 7x + 14     

x = 9

I'll save this one for later...

The magnitude of an angle is the amount of rotation through which one of the arms must be rotated about the vertex to bring it to the position of the other arm.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The magnitude of angle ABC is 150 degrees.

Not so...

First, we calculate the value of x

(6x - 11) + 81 + (x + 5) = 180

x = 15

(4y - 18) + (6x - 11) + (y + 14) = 180

(4y - 18) + (6*15 - 11) + (y + 14) = 180

y = 21

There are 7 isosceles triangles:

1/  ABC

2/  ABD

3/  BCD

4/  BDE

5/  CDE

6/  DEF

7/  CEF

One side of a triangle is one-third of the longest side. The third side is 13 feet less than the longest side. The perimeter is 85. Find all three sides.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

"one side" = x          "long side" = 3x           "third side" = 3x - 13

x + 3x + 3x - 13 = 85

x = 14

sides of a triangle are  14,  42, and 29

Inside a square with a side length of 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. What is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Triangle height: h = √50

Triangle side:  a = h / cos(30º)

Side of a small square: s = a * sin(15º)