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A B C E O D Secants AE and AD intercept arcs BC and ED Angles Formed by Chords, Secants, and Tangents A secant is a line that intersects a circle at two points This diagram shows two secant rays.
A Chords AC and BD intercept two pairs of opposite arcs: AB and DC AD and BC B O C D Intercepted Arcs of Chords
B A Tangents BA and BC intercept arcs AC and ADC C O D Intercepted Arcs of Tangents
y° 1 x° Intercepting Chords Theorem The measure of an angle formed by two chords that intersect inside a circle is half the sum of the measures of the intercepted arcs: m1 = ½ (x + y)
1 y° x° Intercepting Secants Theorem The measure of an angle formed by two secants or tangents that intersect at a point outside the circle is half the difference of the measures of the intercepted arcs: m1 = ½ (x - y)
65° x° 95° Example 1 Find the value of x: x = ½ (95 + 65) = ½ (160) = 80
35° y° 130° Example 2 Find the value of y: 35 = ½ (130 – y) 70 = 130 – y y = 130 – 70 = 60