Number 3 11:04 PM Wed Sep 21=Section 4 The CircleOur second theorem concerns two tangents to a circle drawn from an externalpoint, Fig. 6-68.Two TangentsDrawn to a CircleHere, PA equals PB. Also, angle APC equalsangle BPC.Turning now from tangents to chords, Fig. 6-69, we have the theoremIf two chords in a circle intersect, the product ofthe parts of one chord equals the product of the partsof the other chordHere,IntersectingChordsTwo tangents drawn to a circle from a pointoutside the circle make equal angles with a linedrawn from the circle's center to the externalpoint. The distances from the external pointto each point of tangency are equal.+++ Example 22: Find x in Fig. 6-70.Solution: By theorem 85 we can write刀ab = cd16.3x10.1(12.5)x =:10.1(12.5)16.3= 7.758485SemicircleAny angle inscribed in a semicircle is a right angle.+++ Example 23: Find the distance x in Fig. 6-71.Solution: By statement 82, we know that = 90°. Then, by the Pythagorean theorem,x=√(250)² (148)² = 20182***Exercise 4 The Circle1. Find the circumference and area of a circle of radius 4.82 cm.2. Find the circumference and area of a circle of radius 2.385 in.3. Find the radius and area for a circle whose circumference is 74.8 in.4. Find the radius and area for a circle whose circumference is 2.73 m.5. Find the radius and circumference of a circle whose area is 39.5 ft².6. Find the radius and circumference of a circle whose area is 2.74 m².7. Inscribed and Circumscribed. A polygon is said to be inscribed in a circle ifevery vertex of the polygon lies on the circle. The circle is then said to be cir-cumscribed about the polygon. A polygon is said to be circumscribed about acircle if the circle is tangent to each side of the polygon. The circle is then saidto be inscribed in the polygon.8+1QAA ĘFIGURE 6-68aFIGURE 6-6916.312.5FIGURE 6-700FIGURE 6-71A193/1040B10.1193bSemicircle of radius = 125x91%

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Topic = Circle