Chords AB and AC lie on opposite sides of the center of the circle and form BAC = 72 ° 30.
| April 2, 2021 | education
Chords AB and AC lie on opposite sides of the center of the circle and form BAC = 72 ° 30. Find the values of arcs AB and AC if their ratio is 19:24.
The angle BAC, which the chords form, is 72 ° 30 ‘or 72.50, then the degree measure of the BC arc is twice the angle BAC and is equal to 2 * 72.5 = 145.
The degree measure of the circle is 360, then the sum of the degree measures of the arcs AC and AB are equal:
◡AC + ◡AB = 360 – 145 = 215.
By condition, AB / AC = 19/24.
19 * AC = 24 * AB.
AC = 24 * AB / 19.
24 * AB / 19 + AB = 215.
24 * AB + 19 * AB = 215 * 19 = 4085.
43 * AB = 4085.
AB = 4085/43 = 95.
AC = 24 * 95/19 = 120.
Answer: The magnitude of the arc AB = 95, AC = 120.
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