1) Find the circumradius of triangle ABC if AB=BC=29 and AC=40.
2) In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BC.
3) In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BZ.
4) Angle bisectors AX and BY of triangle ABC meet at point I. Find angle C in degrees, if angle AIB= 106 degrees.
(There were pictures that went along with the problems, but I wasnt able to upload them. Sorry about that.)
Here are some other geometry problems to try!
5) In the trapezoid shown, the ratio of the area of triangle ABC to the area of triangle ADC is 7:2. If AB+CD=210 cm, how long is segment AB?
6) Triangle PAB is formed by three tangents to circle O and angle PAB = 45 . Find angle AOB.
7) In the circle with center Q, radii AQ and BQ form a right angle. The two smaller regions are tangent semicircles, as shown. The radius of the circle with center Q is 15 inches. What is the radius of the smaller semicircle? Express your answer as a common fraction.
8) In a circle, the length of an arc intercepted by a central angle is 12mm, and the radius of the circle is 8mm. What is the measure, in radians, of the angle?
9) Three balls are placed inside a cone such that each ball is in contact with the edge of the cone and the next ball. If the radii of the balls are 20 cm, 12 cm, and r cm from top to bottom, what is the value of r?
10) Right triangle ABC has side lenghts AB = 3, BC = 5. Square XYZW is inscribed in triangle ABC with X and Y on line AB, and Z on line BC. What is the side length of the square.
You should try these problems too!
11) In the right triangle, an altitude is drawn from the right angle to the hypotenuse. Circles are inscribed within each of the smaller triangles. What is the distance between the centers of these circles?
12) An equilateral triangle and a square both have perimeters of 48 inches. What is the ratio of the area of the triangle to the area of the square? Express your answer as a common fraction.
13) The square below has area 100. Find the area of the shaded region
14) In triangle ABC, points D and F are on AB and E is on AC such that DE || BC and EF || CD. If AF = 9 and DF = 2, then what is BD?
15) Points A B and C are on a sphere whose radius is 13. If AB = BC = 12, what is the longest possible value of AC?
3)
In triangle ABC let the angle bisectors be BY and CZ. Given AB=8, AY=6, and CY=3, find BZ.
In the other problem we found that BC = 8
So, again, by the angle bisector theorem
AC / BC = AZ / BZ
9 / 8 = AZ / BZ
So....there are 17 parts to AB
And BZ = 8 of them
So
BZ = (8/17)(AB) = (8/17)(8) = 64 /17
