Two mutually perpendicular chords are drawn in the circle. each of them is divided by the other chord into segments equal to 5 and 11. Find the distance from the center of the circle to the point of intersection of the chords.
From point O, the center of the circle, draw perpendiculars OK and ОМ to cords AB and CD.
The perpendiculars OM and OK, drawn from the center of the circle, divide the chords in half.
Let us determine the length of the chords AB and CD. AB = CD = AH + BH = CH + DH = 5 + 11 = 16 cm.
Then AM = DK = 16/2 = 8 cm.
HM = HK = AM – AH = 8 – 5 = 3 cm.
A quadrangle OMНK is a square, then OH is its diagonal. OH ^ 2 = OM ^ 2 + HM ^ 2 = 9 + 9 = 18.
OH = √18 = 3 * √2 cm.
Answer: From the center of the circle to the point of intersection of the chords is 3 * √2 cm.
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