Question 974341: Hello! My sister is in great need of help with geometric proofs (and I really want to help):
Given: Triangle WXY inscribed in Circle and XY is the diameter
Area of Circle/Area of Triangle WXY = 2 Pi
Find m (XY2)
It must be written under the Givens and the Proofs.
Please help :) Thank you!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Given, a triangle is inscribed in a circle.
Given, the circle has a radius.
Given, the area of the circle is pi*r^2.
Given, a diameter of a circle splits the circle into two 180 degree arcs.
Inscribed angles subtend twice the arc of the angle.
The inscribed angle subtends 180 degrees.
The altitude of this right triangle is perpendicular to the base (definition)
Therefore, the inscribed angle is 90 degrees, and the triangle is a right triangle.
The altitude of the right triangle is a perpendicular from the base. Definition of altitude
The altitude divides the diameter into two equal arcs. Reason: perpendicular to a straight line makes two right angles
The radius is the distance from the center to the angle, and the angle lies on the edge of the circle.
The radius is the altitude. ;; The radius must be perpendicular to the diameter.
Therefore, the area of the triangle is (1/2)bh = (1/2) r*r ; definition of area of triangle; definition of radius.
The area of the circle divided by the area of the triangle is pi*r^2/(1/2)*r^2
The ratio is 2 pi.
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