Question 1067940: Please help me to solve the problem 2)A chord of a circle is 5cm long and subtends an angle of 24.3° in the major segment, calculate (a) the perpendicular distance of the chord from the circle (b) the radius of the circle
Answer by math_helper(2461)   (Show Source):
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Chord AB, in green, is 5cm, the angle subtended is 24.3 degrees. Need to find 'd' and 'r' (note in the above figure, distance d+a = r, because d is the distance from the chord to the circle).
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Let's focus on the right triangle to the right of the y-axis, as in the figure below:
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Half the chord AB is shown, that length is 2.5cm, and the angle DCB is 24.3/2 = 12.15 degrees.
tan(12.15) = 2.5/a —> a = 2.5/tan(12.15) = 2.5/0.215294 = 11.612, 
sin(12.15) = 2.5/r —> r = 2.5/sin(12.15) = 2.5/0.210472 = 11.878, 
Recall d+a = r, so d = r-a = 11.878-11.612 = 0.266, 
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