3.7 Secants and Tangents

Tangent: a line that shares only one point with a circle and is perpendicular to the radius or diameter at that point.

Point of tangency: the point that a tangent shares with a circle

A radius is perpendicular (makes a 90o angle) to the tangent at the point of tangency

Segments

Two tangents Tangents are equal

Tangent and Secant Tangent2 = outer segment(whole secant)

Two Secants Outer segment(whole secant) =

outer segment(whole secant)

Two Chords Segment1 x segment2 = segment1 x segment2

Angles/Arcs

Two Tangents Exterior = ½(arc far away – arc close to angle)

Tangent and Secant Exterior = ½(arc far away – arc close to angle)

Two Secants Exterior = ½(arc far away – arc close to angle)

Two Chords Interior = ½(intercepted arc + intercepted arc)

KL is a radius of circle K. Determine whether LM is tangent to circle K. Justify your answer.

*Do this one on the very back page of the packet. Find x, if EW is a tangent to circle D.

AC and BC are tangent to circle Z. Find the value of x.

Find the perimeter of triangle SQR.

Find x.

Find x.

Find x.

Find the measure of arc BC.

Find the measure of arc XYZ.

* Do this one on the extra space under example 7. Find x.

Find x.

Find x.

Find x.

Find x.

Find x.

Find x.