Problem Solving

Find the diameter
OA is 11

since it is an equidrateral ABC length is 2/3 of its circumference. that means 2/3 πd=24 so d=36/π where π is 3.14 hence d=11

swle24 wrote:since it is an equidrateral ABC length is 2/3 of its circumference. that means 2/3 πd=24 so d=36/π where π is 3.14 hence d=11

thanks for the solution..
Is this based on some properties, haven't come across this before.
Is there something for an isoceles triangle as well?

Hi swle24 can you pls explain how an equilateral triangle covers 2/3 of the circumferecne?? This problem has been in my mind for a very long time!! An explanation would be very helpful!! Thanks

No, the reason for it is based on the fact that a chord makes an angle at the centre that is double the one it makes on the circumference. So, the chord BC which makes 60º at circumference (point A) will make 120º at the centre. So the arc BC is making 120º at centre while arc BAC makes 240º.
Therefore, the arc length BAC is (240/360)*pi*d=24
Cheers