How to find the radius of a circle?
2014-07-24 8:43 pm
A circle and square have the same center. The circle is the exact size that its intersection points with the square trisect each side of the square. If the square has side length 6, what is the radius of the circle?
回答 (1)
2014-07-24 8:58 pm
so, the sq has a side of 6cm
the circle intersects along the side at 2cm, and 4cm, forming a triangle with a base of 2cm
the top angle of this triangle is 30 degrees,
but this isosceles triangle is equivalent to 2 right angle triangles side by side, with a base of 1cm and a top angle of 15 degrees
you can now use the sine rule to work out the hypotenuse - which will also be the radius of the circle
you can also use Pythagoras, as you know the distance from the centre of the square to the edge (3 cm)
the circle intersects along the side at 2cm, and 4cm, forming a triangle with a base of 2cm
the top angle of this triangle is 30 degrees,
but this isosceles triangle is equivalent to 2 right angle triangles side by side, with a base of 1cm and a top angle of 15 degrees
you can now use the sine rule to work out the hypotenuse - which will also be the radius of the circle
you can also use Pythagoras, as you know the distance from the centre of the square to the edge (3 cm)
收錄日期: 2021-04-15 16:03:37
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