Transcript Slide 1
10-4 Circles Given a point on a circle, construct the tangent to the circle at the given point. (Euclidean) 1) Draw ray from O through A A O 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.
Given a point outside the circle, construct a tangent to the circle from given point.
1) Draw OP 2) Find midpoint by making perp bisector.
3) Draw circle with radius MP and center M 4) Draw PX ; X is where the two circles meet O X M P Justification, inscribe triangle in semicircle to get right triangle. Radius OX, XP are 90 o , thus tangent.
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.
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.
Draw two congruent externally tangent circles and draw a rectangle that is tangent to the circles.