Math 444 Quiz #2

Do both problems. The first is a construction and the second is a proof.

Problem 1 (20 points)

The figure below consists of the segment AB and two rays, ray AM and ray BN (with arrow indicators on the ends). Construct with straightedge and compass a circle which is tangent to all 3, the segment and both rays.

Instructions: As last time, label your construction and write a brief description of the steps. Just right enough to make it clear what you did, not why it works.

Problem 2 (20 points)

What you can use.

You can use any of the theorems from B&B Chapters 1-5 (this includes the recent chapter on circles). Don’t assume problems from B&B (especially this one!).

The Problem

1. Given two chords of a circle, AB and CD, which intersect at a point P, find a relationship among the four lengths PA, PB, PC, PD.
2. Then prove that the relationship is true. Hint: Similar triangles.

Answers to Math 444 Quiz #2

Since the circle will be tangent to all three lines or segments, the center is equidistant from each, so the center is on both angle bisectors. Construct the center as the intersection of angle bisectors.

Then construct the radius by dropping a perpendicular to one of the sides.

Back to Problem 1.