GeometryGeometry Lesson 6.1 Chord Properties

Geometry Geometry Angles in a Circle In a plane, an angle whose vertex is the center of a circle is a central angle of the circle. In a plane, an angle whose vertex is on the circle is an inscribed angle of the circle. inscribed angle Q

Geometry Geometry Arc Measures The measure of a minor arc is defined to be the measure of its central angle. 60 ° 180 ° J

Geometry Geometry Chord Central Angle Conjecture If two chords in a circle are , then their central angles are . X  AXB   CXB if and only if 

Geometry Geometry Chord Arcs Conjecture If two chords in a circle are , then their intercepted arcs are . X  if and only if 

Geometry Geometry Chord Distance to Center Conjecture Two  chords in a circle are equidistant from the center of the circle.

Geometry Geometry Perpendicular to a Chord Conjecture The perpendicular from the center of a circle to a chord is the bisector of the chord. is a diameter of the circle.

Geometry Geometry Perpendicular Bisector of a Chord Conjecture The perpendicular bisector of a chord passes through the center of a circle.

Geometry Geometry Summary of Chord Property #2, #3 and #4 A perpendicular line from the center of a chord to the center of a circle: #2: Makes a 90° angle with the chord #3: Creates two equal line segments RS and QR #4: Must pass through the center of the circle O

Geometry Geometry Ex. 1 You can use Theorem 10.4 to find m. Because AD  DC, and . So, m = m 2x = x + 40Substitute x = 40 Subtract x from each side. 2x ° (x + 40) °

Geometry Geometry Ex. 2 AB = 8; DE = 8, and CD = 5. Find CF.

Geometry Geometry Let’s get crazy… b Find b.

Geometry Geometry Let’s get crazy… b Step 1: What do we need to find? We need a radius to complete this big triangle. Find b.

Geometry Geometry Let’s get crazy… b Find b. How do we find a radius? We can draw multiple radii (radiuses).

Geometry Geometry Let’s get crazy… b Find b. How do we find a radius? Now what do we have and what will we do?

Geometry Geometry Let’s get crazy… b Find b. How do we find a radius? We create this triangle but how do we get the missing side?

Geometry Geometry Let’s get crazy… b Find b. How do we find a radius? We create this triangle but how do we get the missing side? 4

Geometry Geometry Let’s get crazy… b Find b. !!!Pythagorean Theorem!!! a 2 +b 2 =c 2 so =169 so b is