8.1 Circle Terminology and Chord Properties This section will introduce you to some of the most important aspects of circle geometry Chord Tangent Diameter Radius

Circle Terminology Circumference – The perimeter of a circle Radius – A segment connecting the center of a circle with a point on the circle Diameter – A segment that goes through the center of the circle and connects to two points on the outside of the circle Chord – A segment whose end points are on the circle Tangent – A line that intersects the circle on exactly one point

Important Formulas The sum of the interior angles of a triangle is 180° The number of degrees in a circle is 360° Circumference = πd = 2πr Area of a circle = πr2 Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of its hypotenuse a2 + b2 = c2 180° 360° c a b

Formulas in Action Example 1: Find angle B Solution 1: ΔABC is isoceles, so ∟B = ∟C ∟A + ∟B + ∟C = 180° 50° + ∟B + ∟B = 180° 2(∟B) = 130° ∟B = 65° Example 2: Find BC Solution 2: Use the Pythagorean Theorem Let BC be x x2 = 52 + 122 x2 = 25 + 144 = 169 x = 169 = 13 Therefore BC = 13 B A 5 50° A C 12 B C

Some Important Chord Properties The Diameter perpendicular to a chord bisects the chord and its arc If AB CD, then CE = ED The perpendicular bisector of a chord passes through the center of the circle If AB CD and AE = EB, then CD passes through the center of the circle A C D E B C A B E D