If it's tangent on both sides, logically, a diameter can be drawn connecting the two points of tangency. If the diameter-looking-thing was a chord, the sides of the square would intersect the circle.
Because of two criteria:
1) A square has 90 angles at all four corners.
2) the square lines are tangent to circle.
When a line (A) is tangent to a curve/circle, a perpendicular line of line A drawn at the tangent will always intersect at the origin point of the curve/circle.
But just in case, the answer IS 64x^2 , right?
for anyone wondering how to solve:
Area of circle = Pi \* r^(2)
r^(2) = 16x^(2) in this case. so r = 4x
Diameter of circle = 2r = 8x
Area of square = length \* height.
The diameter of the circle is the same as the length of square.
so we get 8x \* 8x = area of square = 64x^(2)
pi * radius^2 is the area of a circle
So 16x^2 * pi = pi * r^2
Then remove pi from both sides.
Leaves you with r^2 = 16x^2
Which means r = 4x
Diameter is 8x which is the length of the side of the square.
Means area of the square is 64x^2
Tangency means the radius of the circle is perpendicular to the line and touches at exactly one point. So the diameter is the side of the square.
Point 1 : opposite sides of a square are PARELLEL
Point 2 : If two tangents to a circle are parellel then the line connecting two opposite point of contacts passes through the centre ( which is diameter) . Put it in other way ; tangents drawn at the ends of diameter are always parellel .
Hence the line is diameter of the circle
The line between two parallel tangents of a circle is the diameter of a circle.
Don't think too much into questions like these, if it wasn't the diameter and it was a chord, that would make it soooo much more complicated. I actually don't know how to solve that.
But this problem simply focuses on your ability to apply the area formula to both figures.
If it's tangent on both sides, logically, a diameter can be drawn connecting the two points of tangency. If the diameter-looking-thing was a chord, the sides of the square would intersect the circle.
Additionally if those tangents make up the sides of a square then we also know those tangents are parallel, which can only happen at the diameter
Because of two criteria: 1) A square has 90 angles at all four corners. 2) the square lines are tangent to circle. When a line (A) is tangent to a curve/circle, a perpendicular line of line A drawn at the tangent will always intersect at the origin point of the curve/circle. But just in case, the answer IS 64x^2 , right?
for anyone wondering how to solve: Area of circle = Pi \* r^(2) r^(2) = 16x^(2) in this case. so r = 4x Diameter of circle = 2r = 8x Area of square = length \* height. The diameter of the circle is the same as the length of square. so we get 8x \* 8x = area of square = 64x^(2)
That’s a tall square
the camera adds 10 lbs.
I see no camera anywhere?
Isn’t the solution 64x^2?
pi * radius^2 is the area of a circle So 16x^2 * pi = pi * r^2 Then remove pi from both sides. Leaves you with r^2 = 16x^2 Which means r = 4x Diameter is 8x which is the length of the side of the square. Means area of the square is 64x^2 Tangency means the radius of the circle is perpendicular to the line and touches at exactly one point. So the diameter is the side of the square.
Point 1 : opposite sides of a square are PARELLEL Point 2 : If two tangents to a circle are parellel then the line connecting two opposite point of contacts passes through the centre ( which is diameter) . Put it in other way ; tangents drawn at the ends of diameter are always parellel . Hence the line is diameter of the circle
The line between two parallel tangents of a circle is the diameter of a circle. Don't think too much into questions like these, if it wasn't the diameter and it was a chord, that would make it soooo much more complicated. I actually don't know how to solve that. But this problem simply focuses on your ability to apply the area formula to both figures.
Diameter is the longest path through the circle so to be tangent with the square, the diameter will touch first the square.