Originally Posted by
sa-ri-ga-ma When the two chords Ab and CD intersect each other at E, they satisfy the following condition.
$\displaystyle \frac{AE}{EB} = \frac{CE}{ED}$ .............(1)
AE = 4, AB = 7. So EB = ...?
CD = l, ED = x, so CE = ...?
Substitute these values in equation (1) and simplify.
The equation obtained is
$\displaystyle x^2 - lx + 12 = 0.$ Or
$\displaystyle l = x + \frac{12}{x}$
To get the minimum length of the chord CD, find dl/dx and equate it to zero. Then solve for x. Substitute this value in eq.(1) to find CF, then find CD.