11.2/11.3 Tangents, Secants, and Chords

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11.2/11.3 Tangents, Secants, and Chords Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. Warm-up (IN)

Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. Notes Ex 1 – Scientists want a satellite’s signal to reach 35% of the way around Earth along . To do this, must equal 126°. How far from Earth’s surface should this satellite be? by HL C A B D E 4000 mi

Angles formed by Tangents and Secants – Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. Angles formed by Tangents and Secants – The measure of an angle formed by the intersection of 2 tangents, 2 secants or a secant and a tangent, at a point outside a circle, is half the difference of the measures of the intercepted arcs.

Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. Ex 1 – Find

Arcs formed by intersecting chords – Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. Arcs formed by intersecting chords – The measure of an angle formed by the 2 chords is equal to half the sum of the measures of the intercepted arcs.

Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. Ex 2 – Find the value of x and the measure of each labeled arc or angle.

Chord Bisector Theorems – Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. Chord Bisector Theorems – The perpendicular bisector of a chord passes through the center of the circle. A diameter that is perpendicular to a chord bisects the chord and its corresponding arc.

Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. In a circle, two congruent chords are equidistant from the center of the circle.

Learning Objective: To find arc and angle measures when segments intersect circles and to solve real world problems involving arcs and chords of circles. Ex 3 – Find

HW – Out – Describe two ways to show that two chords are congruent. Summary – Today, I learned… HW –