11-1 tangent lines learning target: i can solve and model problems using tangent lines. goal 2.03
TRANSCRIPT
11-1 Tangent Lines
Learning Target: I can solve and model problems using tangent lines.
Goal 2.03
A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.
The point where a circle and a tangent intersect is the point of tangency.
Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.
AB OP
O
A
P
B
Theorem 11-2 (Converse of thm. 11-1)If aline in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.
O
A
P
B
If all vertices of a triangle lie on the circle, the triangle is inscribed in the circle.
If a circle is inscribed inside a triangle, the triangle is circumscribed about the circle.
Theorem 11-3The two segments tangent to a circle from a point outisde the circle are congruent.AB≅CB
O
B
C
A