Geometry Problem Help Please? WILL pick top answer

[From: ] [author: ] [Date: 11-05-06] [Hit: ]

The radii,an 8 meter segment form the legs of a 30 60 90 triangle and while segmentsfrom the vertices of the triangles to the center of the circle form hypotenuses. The lengths of the radii are therefore8/√3 = 8√3/3 metersThat is approximately 4.61 meters if you need a numerical approximationThe other answerer made a slight scale error in the other direction, his result is EXACTLY TWICEthe correct answer thus the correct answer of8√3▬▬ meters is exactly half of the result that he got........

length of the tangents.

CORRECT ANSWER IS 12√3 and that is EXACTLY TWICE the result he got of 6√3 which is
not correct, only half of the correct answer

Each side of a circumscribed equilateral triangle is 16 meters.
Find the radius of the circle.

The radii of the circle are perpendicular bisectors to the 16 meter triangle sides.
The radii, an 8 meter segment form the legs of a 30 60 90 triangle and while segments
from the vertices of the triangles to the center of the circle form hypotenuses.

The lengths of the radii are therefore 8/√3 = 8√3/3 meters

That is approximately 4.61 meters if you need a numerical approximation

The other answerer made a slight scale error in the other direction, his result is EXACTLY TWICE
the correct answer thus the correct answer of

8√3
▬▬ meters is exactly half of the result that he got.
..3

-

Ok I will answer Geometry Problem

Let one tangent point be X and the other be Y. Let the center of the circle be C.

Angle XPC = angle YPC so they are both 30 degrees.

Triangle XPC is a right triangle with a right angle at X and a 30 degree angle at P
The opposite side from the angle, XC, is length 12

The sine of 30 degrees is 1/2 so 12 is 1/2 of the hypotenuse and the hypotenuse is 24
The tangent segment is the adjacent side so its length is sqrt(24^2 - 12^2) = 6 sqrt(3).

Now I am very upset you have asked two questions instead of one, but I have to answer this one too, or you could end up giving top answer to someone else instead.

Each side is 16 meters. Use the midpoint to make a right triangle with long leg 8.
The angle at the center is 1/6 of a circle which is 60 degrees.
If M is the midpoint, C is the center, and A is on the circle, the triangle looks like

C
|
M-------------A

and angle MCA is 60 degrees, and MA is 8.
radius = CA
CA sin 60 = MA
CA = 8 / (sqrt(3)/2) = 16/sqrt(3) = 9.237 approx.

12

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