Question 3915: area of a regular pentagon inscribed in a circle of radius 12cm.
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! This question is somehow very unclear ,it did not show what the given
conditions are and what you ask for ???
I think it should be given the length of a chord on a circle. Then try
to find the distance from its mid point to the circumference of the circle ?
P
| M
------|-------
A | B
|
|
| O
Here, AB is the chord,O is the center, P is on the circumference of
the circle and M is the midpoint of AB.
We see that OB^2 = MB^2 + OM^2, let AB = L, OB = r.
We have OM = sqrt(r^2 - 1/4 L^2)
and so PM = OP - OM = r - sqrt(r^2 - 1/4 L^2).
Also, I don't think any further explanations are necessary.
Try to figure out the details if you have trouble understanding.
Kenny
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