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Circles

/Tag: Circles
25 11, 2016

Cyclic Quadrilaterals opposite angles of a cyclic quadrilateral are equal   In the diagram, 0 is the centre of the circle and AB║AD and BC meet at P. Prove: a. CP = DP b. DABP is isosceles c. OAPC is a cyclic quadrilateral. a. ∠PCD = ∠ABC     (corresponding [...]

26 10, 2016

Circles

By |2016-10-26T16:45:32+10:00October 26th, 2016|Tags: , , |Comments Off on Circles

Circles x2 + y2 = r2 Centre (0, 0) Radius = r units Domain: -r ≤ x ≤ r Range: -r ≤ y ≤ r worked examples For the circle with equation x2 + y2 = 16, find: a. the centre b. the radius c. the domain [...]

11 09, 2016

Circles & Lines

Circles & Lines Perpendicular distance = radius, then tangent Perpendicular distance < radius, line intersects circle at 2 points Perpendicular distance > radius, line does not intersect with the circle   x2 + y2 = r2    Circle centre (0, 0) radius = r units (x - a)2 + [...]

5 07, 2016

Area Of Sector

By |2016-10-21T13:17:00+10:00July 5th, 2016||Comments Off on Area Of Sector

Area of Sector $A=\frac{\theta}{360}\,\pi r^2$ worked examples Find the area of a sector with angle of 50° and a radius of 10cm, correct to 2 decimal places. $A=\frac{50}{360}\times\pi \times 10^2$ Using the formula $A=\frac{\theta}{360}\,\pi r^2$ where θ = 50 and r = 10 A = 43.6332313 calculate A = 43.63cm2 round [...]

5 07, 2016

Perimeter Sector

By |2016-10-21T13:17:00+10:00July 5th, 2016||Comments Off on Perimeter Sector

Perimeter Sector $P=\frac{\theta}{360}\times2\pi\, r+2r$ worked examples Find the perimeter of this sector, correct to 2 decimal places $P=\frac{50}{360}\times2\pi\, \times12+2\times12$ r = 12cm and the angle at the centre = 50°, hence θ = 50 substitute into the forumla $P=\frac{\theta}{360}\times2\pi\, r+2r$ L = 34.47cm calculate further examples [...]

26 06, 2016

Arc Length

By |2016-10-21T13:17:02+10:00June 26th, 2016||Comments Off on Arc Length

Arc Length $L=\frac{\theta}{360}\times2\pi r$ worked examples Find the length of the arc in this sector. $L=\frac{50}{360}\times2\times\pi\times 12$ r = 12cm and the angle at the centre = 50°, hence θ = 50 substitute into the forumla $L=\frac{\theta}{360}\times2\pi r$ L = 10.47cm calculate further examples [...]

26 06, 2016

Circumference Of Circle

By |2016-10-21T13:17:02+10:00June 26th, 2016||Comments Off on Circumference Of Circle

Circumference Of Circle $C=\pi\,d$   or   $C=2\pi\, r$ Areas and Circumference of Circles The radius of a circle is half the diameter. The diameter of a circle is twice the radius. The Area of a circle is given by the formula $A=\pi r^2$ The Circumference of a circle is given by the [...]

19 06, 2016

Circle Geometry

Circle Geometry Go to the Circle Geometry to see more questions or ask your own Topics Covered in Circle Geometry Parts Of A Cirlce Arcs, Angles & Chords Chord Properties Concyclic Points Cyclic Quadrilaterals Tangent Properties Formulas Used [...]

25 08, 2015

Annulus

By |2016-10-21T13:17:10+10:00August 25th, 2015|Tags: , , , , |Comments Off on Annulus

Area of Annulus $A=\pi (R^2-r^2)$ the annulus is the area between two circles, the 'donut' $A=\pi(R^2-r^2)$ $R=\sqrt{\frac{A}{\pi}+r^2}$ $r=\sqrt{R^2-\frac{A}{\pi}}$ worked examples Find the area between two circles, with inside radius of 10cm and an outer radius of 15cm. $A=\pi\times(15^2-10^2)$ A = 392.7cm2 R = 15cm r = 10cm Find the [...]

25 08, 2015

Circles

By |2016-10-21T13:17:10+10:00August 25th, 2015|Tags: , , , |Comments Off on Circles

Area of Circle $A=\pi r^2$ $C=\pi d$   or   $C=2\pi r$ Areas and Circumference of Circles The radius of a circle is half the diameter. The diameter of a circle is twice the radius. The Area of a circle is given by the formula $A=\pi r^2$ The Circumference of a circle is given [...]