Warm up! Find the perimeter of the shaded region.

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Presentation transcript:

Warm up! Find the perimeter of the shaded region.

Find the area of the shaded sector. Practice: Find the area of the shaded sector. R Q 12 yd

Queeeeez time

LG 1-3 Circle Theorems

Learning goal questions How are Congruent Chords related? How does the location of the vertex of an angle effect the formula for finding the angle measure? When two lines intersect they create an angle. How does the location of the vertex of that angle effect the formula that I will use to find the lengths of those line segments that get created?

terminology Inscribed Angle: an angle whose vertex is on the circle and whose sides contain chords of a circle Tangent Line: a line in the plane of a circle that intersects a circle at only one point, the point of tangency Secant Line: a line in the plane of a circle that intersects a circle at exactly two points Secant Segment: a segment that contains a chord of a circle and has exactly one endpoint outside of the circle Vertical angles Linear Pair Supplementary

Secant Line: intersects the circle at exactly TWO points

Tangent Line: a LINE that intersects the circle exactly ONE time Forms a 90°angle with one radius Point of Tangency: The point where the tangent intersects the circle

Secant Radius Diameter Chord Tangent Name the term that best describes the notation. Secant Radius Diameter Chord Tangent

In a circle or in congruent circles, two minor arcs are congruent Arcs and Chords Theorem In a circle or in congruent circles, two minor arcs are congruent if and only if (iff) their corresponding ______ are congruent. chords A D AD  BC iff B AD  BC C

Warm up Find the value of x and y. 120  = 120 x  y = 60 

Graphic Organizer for Angle Theorems

Circle P has a radius of 5 units, and circle T has a radius of 3 units. If QR = 1, find the following measures: RT PQ AB R P Q T B A

The vertices of isosceles triangle ABC are located on circle R. Arcs and Chords The vertices of isosceles triangle ABC are located on circle R. If BA  AC, identify all congruent arcs. A BA  AC R C B

x = 3 5x = 2x + 9 3x = + 9 In J, m3 = 5x and m 4 = 2x + 9. Find the value of x. 5x = 2x + 9 3x = + 9 x = 3

x = 22 112  1) If measure of JK = 80 and JMK = 2x – 4, find x. 2) If mMKS = 56, find measure of arc MS. 112 

Practice and HOMEWORK!