Angles and Segments – Angles Formed by Chords Secants and Tangents

Angles formed by Chords, Secants, and Tangents

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Students learn the following theorems related to chords, secants, and tangents. The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs. The measure of an angle formed by two secants drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs. The measure of an angle formed by two tangents drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs. The measure of an angle formed by a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs. Students are then asked to find the missing measures of arcs and angles in given circles using these theorems.
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