SOLUTION: In a circle with a 12-inch radius, find the length of a segment joining the midpoint of a 20-inch chord and the center of the circle

Question 947424: In a circle with a 12-inch radius, find the length of a segment joining the midpoint of a 20-inch chord and the center of the circle

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Use two-dimensional coordinate geometry.

x^2+y^2=12^2 the circle, and you have a possible coordinate x=10 and x=-10; what is the value of y for either of these coordinates? The midpoint of the chord will be on the positive y-axis.

Draw the graph.

You can find your result algebraically letting x=10, and solve the circle equation for y.
Answer by MathTherapy(10553) (Show Source): You can put this solution on YOUR website!

In a circle with a 12-inch radius, find the length of a segment joining the midpoint of a 20-inch chord and the center of the circle

Two of the radii of the circle, along with the chord (base segment) form an isosceles triangle.
One of the congruent sides (radius of circle), the segment being sought, and of the 20" base,
or 20" chord, form a right-triangle. Thus we have a right-triangle with hypotenuse: 12, one leg: 10,
and the segment joining the center of the circle, and the midpoint of the chord, or h.
We then get:

Segment joining the center of the circle, and the midpoint of the chord, or , or , or
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