High School Problem Set

Solve the following problems. Show complete solutions. Be prepared to discuss this tomorrow. To be collected at 9AM.

1. 1. ABCDE is a regular pentagon. AC and BD intersect in F. What is the measure of angle AFB?

   2. Two tangents PA and PB to a circle O (A and B are points on the circle) are drawn from a point outside the circle. If the tangents form a 46 degree angle, what is the measure of angle AOB?

   3. A point is 12 cm from the center of a circle with radius of 15 cm. Find the lengths of the longest and shortest chords that can be drawn through this point.

   4. In a circle, a chord 12 cm long is parallel to a tangent and bisects the radius drawn to the point of tangency. How long is the radius?

   5. A chord, 18 cm long is perpendicular to a radius of a circle. The distance from the intersection of chord and radius to the outer end of the radius is 3 cm. Find the length of the radius.

   6. Triangle ABC has side lengths AB = 65, BC = 33, and AC = 56. Find the radius of the circle tangent to sides AC and BC and to the circumcircle of triangle ABC.

   7. Convex quadrilateral ABCD has sides AB = BC = 7, CD = 5, and AD = 3. Given additionally that ÐABC=60˚, find BD.

   8. Find the distance between the centers of the inscribed and circumscribed circles of a right triangle with sides of length 3, 4 and 5.