Chapter 7 Circles

Circle – the set of all points in a plane at a given distance from a given point in the plane. Named by the center. Radius – a segment from a point on the circle to the circle’s center Congruent circles – two or more circles that have the same radius. Concentric circles- two or more circles that share the same center.

Arc of a circle – consists of two points on the circle and the continuous (unbroken) part of the circle between the two points.

Semicircle – an arc of a circle whose endpoints are the endpoints of the diameter. Minor Arc- an arc of a circle that is less than a semicircle of the circle. Major Arc – an arc of a circle that is greater than a semicircle of the circle.

Chord – a segment that connects two points on a circle.

Diameter – a chord that intersects the center of the circle.

Secant – a line that intersects a circle at two points.

Tangent – a line that intersects a circle at one point.

Inscribed angle – an angle whose vertex and two points intersect the circle.

Central angle – an angle that the vertex is at the center of the circle.

Lesson 7.2 C 61 If two chords in a circle are congruent then they determine two central angles that are congruent.

Intercepted arc – the arc between the points of a central angle.

C -62 If two chords in a circle are congruent, then their intercepted arcs are congruent.

C – 63 The perpendicular from the center of a circle to a chord is the perpendicular bisector of the chord.

C – 64 Two congruent chords in a circle are equally distant from the center of the circle.

C – 65 The perpendicular bisector of a chord passes through the center of the circle.

Lesson 7.3 Tangent circles – Two circles that are tangent to the same line at the same point. Externally tangentInternally tangent

C 66 A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

C 67 Tangent segments to a circle from a point outside the circle are congruent.

Lesson 7.4 C 68 The measure of an inscribed angle in a circle is half the measure of the arc it intercepts.

C – 69 Inscribed angles that intercept the same arc are congruent.

C – 70 angles inscribed in a semicircle are right angles.

C 71 – The opposite angles of a quadrilateral inscribed in a circle are supplementary.

C – 72 Parallel lines intercept congruent arcs on a circle.

Lesson 7.5 C – 73 If C is the circumference and D is the diameter of a circle, then there is a number π such that C = Dπ. Because D = 2r where r is the radius, then C = 2r π (Circumference Conjecture)

Lesson 7.7 Length of an Arc – some fraction of the circumference of its circle. C – 74 The length of the arc equals the degree measure of the arc divided by 360°, times the circumference of the circle. (Arc Length Conjecture)