Lesson 4: 9-5 Tangents

Do circles necessarily need to be touching in order to have common tangents?

If two circles share a common center, but are not the same size, do they have a common tangent or tangents? Explain.

Do you think three circles can share a common tangent?

Tangent
point of tangency
common tangent

G.C.2 Identify and describe relationships among inscribed angles, radii, and chords.

G.C.4 Construct a tangent line from a point outside a given circle to the circle.

A tangent intersects a circle in exactly one point. This point is called the point of tangency. More than one line can be tangent to the same circle. Circles can be inscribed in polygons, just as polygons can be inscribed in circles. if a circle is inscribed in a polygon, then every side of the polygon is a tangent to the circle.

The first bicycles were moved by pushing your feet on the ground. Modern bicycles use pedals, a chain, and gears. The chain loops around circular gears. The length of the chain between these gears is measured from the points of tangency.

If a circle is tangent to one or more of the sides of a polygon dos not mean that the polygon is circumscribed about the circle.

Remind students that they should not assume that a segment that appears to be tangent to a circle is tangent, unless you are told so. The figure must either have a right angle symbol or include the measurements that confirm a right angle.

Social/interpersonal learners. Organize students in small groups. Explain that a company wants to market a new toy with a diameter of 5 inches. Their task is to design a container for the toy that takes up the least amount of shelf space. The container must have flat sides, and therefore cannot be circular. Have students draw and label the circular toy and the container surrounding it. if the display shelf is 3 feet by 10 feet, how many toy containers will fit in a single layer on the shelf? Which shape will allow the maximum number of toys to be displayed on the shelf?

Extension. A circle is circumscribed about a square. The radius of the circle is r. Have the students write an expression for the perimeter of the square in terms of r.

Formative Assessment 

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