Explanation:
there are 2 formulas to calculate the length of a chord, depending on what pieces of information we have.
here now we have the length of the chord, which we need to find the radius, which we need to find the angle at the center.
chord length = 2×sqrt(r² - d²)
chord length = 2×r×sin(c/2)
r is the radius, d is the distance of the chord from the center of the circle, c is the angle of the chord at the center of the circle.
20 =2×sqrt(r² - 12²) = 2×sqrt(r² - 144)
10 = sqrt(r² - 144)
100 = r² - 144
244 = r²
r = 15.62049935... cm
20 = 2×r×sin(c/2) = 2×15.62049935...×sin(c/2)
10 = 15.62049935...×sin(c/2)
sin(c/2) = 10/15.62049935... = 0.6401844...
c/2 = 39.80557109...°
c = 79.61114218...° ≈ 79.6°
(a) the angle subtended by the chord at the center of the circle is about 79.6°.
(b)
the arc length of a segment is 2pi×r × c/360
in our case
2×3.142×15.62049935...×79.61114218.../360 =
= 21.70713182... cm
the whole perimeter of the segment is then arc length + chord length =
= 21.70713182... + 20 = 41.70713182... ≈ 41.7 cm
the perimeter of the minor segment cut off by the chord is about 41.7 cm.