Sect 12 2 Properties of Tangents Geometry Honors

Sect. 12 -2 Properties of Tangents Geometry Honors

What and Why • What? – Find the relationship between a radius and a tangent, and between two tangents drawn from the same point. – Circumscribe a circle • Why? – To use tangents to circles in real-world situations, such as working in a machine shop.

Tangents to Circles • We have looked at the tangent of an angle in a right triangle. Now we will look at the properties of a tangent to a circle. • 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.

Continued •

Theorem 12 -2 •

Example •

Example • Machine Shop – A belt fits tightly around two circular pulleys. Find the distance between the centers of the pulleys.

Example Continued •

Theorem 12 -3 Converse of Theorem 12 -2 •

Example •

Circumscribing Circles • In the figure, the sides of the triangle are tangent to the circle. The triangle is circumscribed about the circle. The circle is inscribed in the triangle.

Theorem 12 -4 •

Example •

Example • The diagram represents a chain drive system on a bicycle. Is BC = GF?

Solution •