Problem is : There is circle of radius 17 cm and there is a point inside the circle such that its distance is 12 cm from center, How many chords can drawn to this point whose length is an integer?
What's the approach? I think infinite, is it right?
[Math] How to calculate total number of chords, if radius of circle given and length of chord is given
circlesgeometryspherical coordinates
Related Solutions
Here is a hint:
You have $\dfrac{a}{r} = \sin \alpha$ and $\dfrac{b}{r} = \cos \alpha$.
You may have to take into account that some of these are half what you are interested in.
Another similar approach may be arisen as following: ${}{}{}{}{}{}{}{}{}{}{}{}{}{}{}$
Best Answer
HINT: the maximal length is that of a diameter passing through the point and the center of the circle, that is to say $34$ cm. The minimal length is that of the chord perpendicular to this diameter. To calculate the length of this minimal chord, connect its edges with the center and trace the perpendicular from the center to the chord. You get two equal right triangles whose hypothenuse is the radius ($17$ cm) and whose one leg is the distance between the point and the center ($12$ cm). So you get that the length of the minimal chord is $2 \sqrt {17^2-12^2} \approx 24.1 \, \,\,\,$. Now simply count how many integers there are between these two values, reminding that you can start from the maximal chord (i.e. the diameter) and progressively rotate to get decreasing chords in two opposite directions.