body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Secants, Tangents, and Angle Measures

Continue to next subchapter

Exercise 36 Page 766

Recall the equation relating the angles between the lines and the measures of the intercepted arcs.

See solution.

Practice makes perfect

Let's consider a circle, a tangent to the circle, and a secant such that they intersect outside the circle.

A circle, a tangent and a secant intersecting outside the circle

To find the value of x we will apply Theorem 10.14.

Theorem 10.14
If two secants, a secant and a tangent, or two tangents intersect in the exterior of a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

In our case, we have that x is equal to half the difference between the measures of arcs QT and PT. m∠ A = x = 1/2(mQT - PT)

Subchapter links

Exercises p.763-767