Q: Does a triangle need to be completely in the circle to be inscribed?

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Yes, but which centre: the centroid, incentre or orthocentre? You need the incentre.

If the sides of the triangle are equal in length to the radius of the circle, then you can simply place the two ends of the hypotenuse on the perimeter of the circle, and it's remaining corner will lie at the circle's center.

the perpendicular bisector

You will need... A set of compasses (for drawing the circle), and a straight edge. First, draw the circle. Then - put the point of the the compasses on the line. Mark the circle where the pencil crosses it. Place the point on this intersection and repeat the action until you're back at your starting point. Now - using the straight edge, join every alternate point to each other - forming an equilateral triangle.

Use the good old formula for the area of a circle:Area = (pi) x (radius)2You need to know the radius, right ? Well, if the circle is inscribed in a square,you're supposed to be able to notice that the length of the side of the squareis the same as the diameter of the circle. The radius is just half of the diameter,so you have everything you need to calculate the area.(I'm absolutely positive that whoever assigned you the problem told you the lengthof the sides of the square.)

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You cannot show it in general since it need not be true!

An equilateral triangle is always inscribed in a circle.This means that if you can prove that z1, z2 and z3 are the vertices of an equilateral triangle, they automatically lie on a circle subscribing it.Compute |z1-z2|, |z1-z3| and |z2-z3|. These need to be equal for z1, z2 and z3 to lie on an equilateral triangle. If not, they aren't lying on an equilateral triangle.for z=a+ib, |z| = (a^2+b^2)^(1/2).To find the center c of the circle, note that (z1-c)+(z2-c)+(z3-c) = 0, hence,c = (z1+z2+z3)/3.

Yes, but which centre: the centroid, incentre or orthocentre? You need the incentre.

If the sides of the triangle are equal in length to the radius of the circle, then you can simply place the two ends of the hypotenuse on the perimeter of the circle, and it's remaining corner will lie at the circle's center.

If I understand your question correctly, you would need to subtract the area of the inscribed circle from the circumscribed circle. Which would approximately be 78.60cm squared.

I'm sorry, but I can not completely answer this question. The length varies from the size of the triangle. I would need a picture to answer this.

The triangle has a perimeter of 3 cm. If the circle rolls along a straight line of length 3 cm without slipping, it would need to make three complete turns. The perimeter of the triangle also makes another turn (sum of external angles = 360), so the circle will need to make 4 turns in all.

PS2Square, Circle, Triangle, Square, Circle, Triangle, Square: All parksSquare, Circle, Triangle, Square, Circle, Triangle, Triangle: All ridesSquare, Circle, Triangle, Square, Circle, Triangle, X: Extra $50,000Xbox NOT THE 360UnlockablesEnter these codes during game play (you do not need to pause the game).[X], [B], [Y], [X], [B], [Y], [A]: $50,000 (do multiple times to get loads of money)[X], [B], [Y], [X], [B], [Y], [X]: All Parks[X], [B], [Y], [X], [B], [Y], [Y]: All Rides[X], [B], [Y], [X], [B], [Y], [B]: Get gold on MissionsNote there is no thrill-ville for xbox360 or wii

do the cheat for lock stars the (it wont unlock but that is helpful) the code is (CIRCLE, RIGHT, CIRCLE, RIGHT, LEFT, SQUARE, TRIANGLE, UP) then get the rhino (Circle, Circle, L1, Circle, Circle, Circle, L1, L2, R1, Triangle, Circle, Triangle) and set the cheat for cars fly (square, down, L2, up, L1, circle, up, x, left) then you need the parachute as the first time i tried this i pressed triangle and died the code is (Left, Right, L1, L2, R1, R2, R2, Up, Down, Right, L1) Then take off in some space and fly around the hole map the police will come but wont damage your tank. If they do press triangle with your parachute on (it will go on you when you do the code and press circle until it opens. eventually you will unlock the hole map after flying around it.

the perpendicular bisector

You will need... A set of compasses (for drawing the circle), and a straight edge. First, draw the circle. Then - put the point of the the compasses on the line. Mark the circle where the pencil crosses it. Place the point on this intersection and repeat the action until you're back at your starting point. Now - using the straight edge, join every alternate point to each other - forming an equilateral triangle.

Front disk breaks pads need replaced.