1. 10-4 Circles Given a point on a circle, construct the tangent to the circle at the given point. (Euclidean) A O 1) Draw ray from O through A 2) Construct a line perpendicular to OA through A. Justification, tangent line is perpendicular to radius, so we make a line perpendicular to radius on the circle.

2. Given a point outside the circle, construct a tangent to the circle from given point. P O 1) Draw OP 2) Find midpoint by making perp bisector. M 3) Draw circle with radius MP and center M 4) Draw PX ; X is where the two circles meet X Justification, inscribe triangle in semicircle to get right triangle. Radius OX, XP are 90 o, thus tangent.

3. Given a triangle, circumscribe a circle. Make circumcenter (perpendicular bisectors) Skipping this step for now. From circumcenter, make radius to vertex, make circle. Circumcenter equidistant to all vertices. Radius all the same, make a circle.

4. Given a triangle, Inscribe a circle. Make incenter (angle bisector) Skip step for now. From incenter, drop a perpendicular, make radius from intersection, make circle. Point from incenter is equidistant to the sides.

5. Draw two congruent externally tangent circles and draw a rectangle that is tangent to the circles.

6. HW #22: Pg 395: 1-10, 12-19