Hi everyone, I'm having struggle to find out how to do this question...
1. Equilateral Triangle inscribed in circle (as the attachment of question.jpg, question 9)
2. According mathopenref.c0m/trianglecentroid.html (please exchange 0 to o to access the urI), one of the Centroid facts mentioned this
"The centroid is exactly two-thirds the way along each median. Put another way, the centroid divides each median into two segments whose lengths are in the ratio 2:1, with the longest one nearest the vertex. These lengths are shown on the one of the medians in the figure at the top of the page so you can verify this property for yourself."



Since centroid divides each median into two segments with 2:1 ratio.
if A to O is 4 (as the attachment of math.jpg), O to X will be 2?? Am I getting the right understanding??

In the figure below, equilateral triangle ABC is inscribed in the circle O, whose radius is 4. Altitude BD is extended until it intersects the circle at E. What is the length of DE ?

A) 1

B) \(\sqrt{3}\)

C) 2

D) \(2\sqrt{3}\)

E) \(4\sqrt{3}\)




As for question 9 since radius is 4, therefore BO = 4.
With 2:1 ratio, OD will be 2. (If I get the correct understanding from the facts)
OE - OD = DE
therefore 4 - 2 = DE
Answer is C
Am I right??