8 1 Circle Terminology and Chord Properties This

8. 1 Circle Terminology and Chord Properties This section will introduce you to some of the most important aspects of circle geometry Chord Diameter Radius Tangent

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 360° 2 Area of a circle = πr Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of its hypotenuse a 2 + b 2 = c 2 c a b

Formulas in Action • Example 1: Find angle B • B A 5 50° A B C • Solution 1: - ΔABC is isoceles, so ∟B = ∟C ∟A + ∟B + ∟C = 180° 50° + ∟B = 180° 2(∟B) = 130° ∟B = 65° 12 C

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