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Angles Formed by Chords, Secants, and Tangents

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.

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Angles Formed by Chords, Secants, and Tangents

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  1. 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.

  2. 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

  3. B A Tangents BA and BC intercept arcs AC and ADC C O D Intercepted Arcs of Tangents

  4. 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: m1 = ½ (x + y)

  5. 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: m1 = ½ (x - y)

  6. 65° x° 95° Example 1 Find the value of x: x = ½ (95 + 65) = ½ (160) = 80

  7. 35° y° 130° Example 2 Find the value of y: 35 = ½ (130 – y) 70 = 130 – y y = 130 – 70 = 60

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