Презентация на тему "Circles 2"

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  Circle

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  A circle is a set of points which are all a certain distance from a fixed point known as the centre. A line joining the centre of a circle to any of the points on the circle is known as a radius. The circumference of a circle is the length of the circle. The circumference of a circle = 2 × π × the radius.

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  The radius of a circle is the distance from the center of the circle to the outside edge.

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  The diameter of a circle is longest distance across a circle. (The diameter cuts through the center of the circle. This is what makes it the longest distance.)

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  The circumference of a circle is the perimeter -- the distance around the outer edge. Circumference = where r = the radius of the circle and pi = 3.141592... The area of a circle Area = where r = the radius of the circle and pi = 3.141592...:

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  A chord of a circle is a line segment that connects one point on the edge of the circle with another point on the circle. (The diameter is a chord -- it's just the longest chord!)

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  An arc of a circle is a segment of the circumference of the circle.

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  Arc length of a circle in radians: Arc Length = Arc length of a circle in degrees: Arc Length =

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  A sector of a circle is a pie shaped portion of the area of the circle. Technically, the piece of pie is between two segments coming out of the center of the circle.

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  Sector area of a circle in radians: Sector Area = Sector area of a circle in degrees: Sector Area =

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  The red line in the diagram is called a chord. It divides the circle into a major segment and a minor segment.

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  Rules 1) When a chord subtends (makes) an angle at the circumference, the angle subtended at the centre (from the same chord) is twice as big:

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  2) A diameter subtends a right–angle at the circumference: 3) Angles subtended onto the circumference in each segment are equal. Angles in opposite segments add up to 180: 4) Tangents drawn from two outside points create two congruent right–angle triangles:

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  5) Angle between a chord and a tangent is equal to the angle subtended at the circumference in the opposite segment: