Task 3: Complete the Proof. (Unit 3, 7.7) Given: Congruent circles OP and OO have a chord AB on both circles. Prove: PO is a perpendicular bisector of AB Options (Sgome may not be used): Given Perpendicular Bisector Theorem Converse of Perpendicular Bisector Theorem Definition of Perpendicular Bisector Definition of Radius All radii of the same circle are congruent. Definition of equidistant Statements Reasons 1. Congruent circles OP and OO, chord AB is on both circles 1. 2. PA, PB, OA, and OB are radii of the circles. 2. By construction of the radius/definition of radius 3. PA PB 3. OAN OB 4. 4. Point P is equidistant from points A and B. Point O is equidistant from points A and B. 5. Point P and Point O lie on the perpendicular bisector of AB 5. 6. PO is a perpendicular bisector of AB 6. Task 4: Find the radius of the congruent circles. Round to the nearest hundredth. (7 7)
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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