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3. Find the radius and area for a circle whose circumference is 74.8 in.

3. Find the radius and area for a circle whose circumference is 74.8 in.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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11:04 PM Wed Sep 21 = Section 4 The Circle Our second theorem concerns two tangents to a circle drawn from an external point, Fig. 6-68. Two Tangents Drawn to a Circle Here, PA equals PB. Also, angle APC equals angle BPC. Turning now from tangents to chords, Fig. 6-69, we have the theorem If two chords in a circle intersect, the product of the parts of one chord equals the product of the parts of the other chord Here, Intersecting Chords Two tangents drawn to a circle from a point outside the circle make equal angles with a line drawn from the circle's center to the external point. The distances from the external point to each point of tangency are equal. +++ Example 22: Find x in Fig. 6-70. Solution: By theorem 85 we can write 刀 ab = cd 16.3x10.1(12.5) x = : 10.1(12.5) 16.3 = 7.75 84 85 Semicircle Any 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 = 201 82 *** Exercise 4 The Circle 1. 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 if every 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 a circle if the circle is tangent to each side of the polygon. The circle is then said to be inscribed in the polygon. 8+1 QAA Ę FIGURE 6-68 a FIGURE 6-69 16.3 12.5 FIGURE 6-70 0 FIGURE 6-71 A 193/1040 B 10.1 193 b Semicircle of radius = 125 x 91%
Transcribed Image Text:11:04 PM Wed Sep 21 = Section 4 The Circle Our second theorem concerns two tangents to a circle drawn from an external point, Fig. 6-68. Two Tangents Drawn to a Circle Here, PA equals PB. Also, angle APC equals angle BPC. Turning now from tangents to chords, Fig. 6-69, we have the theorem If two chords in a circle intersect, the product of the parts of one chord equals the product of the parts of the other chord Here, Intersecting Chords Two tangents drawn to a circle from a point outside the circle make equal angles with a line drawn from the circle's center to the external point. The distances from the external point to each point of tangency are equal. +++ Example 22: Find x in Fig. 6-70. Solution: By theorem 85 we can write 刀 ab = cd 16.3x10.1(12.5) x = : 10.1(12.5) 16.3 = 7.75 84 85 Semicircle Any 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 = 201 82 *** Exercise 4 The Circle 1. 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 if every 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 a circle if the circle is tangent to each side of the polygon. The circle is then said to be inscribed in the polygon. 8+1 QAA Ę FIGURE 6-68 a FIGURE 6-69 16.3 12.5 FIGURE 6-70 0 FIGURE 6-71 A 193/1040 B 10.1 193 b Semicircle of radius = 125 x 91%
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