Two mutually perpendicular chords are drawn in the circle, each of which is divided by another chord into segments 4 and 6. Find the distance from the center of the circle to each chord.
The perpendiculars OH and OK, drawn from the center of the circle to the chords AB and CD, divide them in half.
AK = BK = AB / 2 = (AM + BM) / 2 = 10/2 = 5 cm.
DH = CH = CD / 2 = (DM + CM) / 2 = 10/2 = 5 cm.
The length of the segment KM = AM – AK = 6 – 5 = 1 cm.
The length of the segment NM = DM – DH = 6 – 5 = 1 cm.
Quadrangle OHMK is a rectangle with opposite sides equal, then OK = HM = 1 cm, OK = KM = 1 cm.
Answer: The distance from the center of the circle to the chords is 1 cm.
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