The chords KM and TP of the circle intersect at point A. Calculate the degree measure of the obtuse angle formed by these chords, if K, M, T, P divide the circle into arcs, the degree mkry of which are proportional to the numbers 2,3,6,9
The full circle is 360 degrees.
Let the degree measure of the arc KT = 2 * X0, then, by condition, the arc TM = 3 * X0, MP = 6 * X0, KP = 9 * X0.
Then: 2 * X + 3 * X + 6 * X + 9 * X = 360.
20 * X = 360.
X = 360/20 = 180.
Then the degree measures of the arcs will be equal:
CT = 2 * 18 = 36.
TM = 3 * 18 = 54.
MP = 6 * 18 = 108.
KP = 9 * 18 = 162.
The value of the angle formed by the intersection of two arcs is equal to the half-sum of the degree measures of the opposite arcs.
Angle KAP = TAM = (KP + TM) / 2 = (162 + 54) / 2 = 108.
Answer: The obtuse angle between the chords is 108.
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