The chord divides the circle into two parts, the degree values of which are related as 4: 5.

| February 11, 2021 | education

The chord divides the circle into two parts, the degree values of which are related as 4: 5. At what angles is this chord visible from the points of the circle?

Let the degree measure of one arc formed by the chord AB is equal to 4 * X0, then the degree measure of the other arc will be 5 * X0.

Since the degree measure of the circle is 360, then 4 * X + 5 * X = 360.

9 * X = 360.

X = 360/9 = 40.

Then the degree measure of the smaller arc is 4 * 40 = 160, of the larger arc is 5 * 40 = 200.

The inscribed angle is equal to half the degree measure of the arc on which it rests.

Then the chord AB will be visible from point D, located on a smaller arc (4 * X) will be visible at an angle of 200/2 = 100, and from point C, located on a larger arc (5 * X), at angles 160/2 = 80 …

Answer: The chord is visible at angles of 80 and 100.



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