E Prove each statement. 1. The measure of an angle formed by a secant and a tangent to a circle intersecting at a point in the exterior of the cir- cle is half the difference of the measures of the intercept- ed arcs. 2. If a secant containing the center of a circle is perpendicu- lar to a chord, then it bisects the chord. 3. If a secant containing the center of a circle bisects a chord that is not a diameter, the secant is perpendicular to the chord. 4. If PQ is a diameter of circle O, prove that the tangents to the circle at points P and Q are parallel. 5. In the figure, ACRS is inscribed in a circle with center O, and diameter CE 1 chord RS at point L. Prove that ZCOR = ZCOS. R.
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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