Finding the Distance Between Two Diametrically Opposite Points on a Cone base circle The question is as follows: > Both the slant height and the base diameter of a cone are 12 inches. What is distace between two opposite points on base circle of cone, if it is required that the path must lie on the lateral surface of the cone? I am not sure of where to start with this problem, therefore, any help with how to start this will be very much appreciated. Thank you in advance.

The answer is best seen on a development.

Semi-vertcal angle is $\sin^{-1}\frac12 = 30^{\circ}$

On development angle subtended at cone apex is

$$ \frac12* 360^{\circ}=180^{\circ}$$

If $l=2r = 12 inches, \, $say, cone develpment is a semi-circle of r= 6 units radius.

Minimum (geodesic) distance is shown by red line $$ = r \sqrt 2 \, or \, 6\sqrt 2 $$

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