Circle Theorems A Circle features. Circumference Diameter Radius from the distance across around centre passing of the circle the circle,
Circle to any point on the of through the centre circumference the its circle PERIMETER A Circle features.
Major Segment Ch or d AR C Minor Segment
part joining the touches two a lineofwhich circumference points on the of a at the circumference circle circumference. one
point only chord divides circleto From Italian tangere, into two segments touch Tan g
ent Properties of circles When angles, triangles and quadrilaterals are constructed in a circle, the angles have certain properties We are going to look at 4 such properties before trying out some questions together An ANGLE on a chord An Alternatively
that Angles sits on a Weangle say Angles chord subtended does by notan arc as achange chord the in the
APEX same moves segment around the are circumference equal as long as it stays in the same segment From now on, we will only consider the CHORD, not the ARC
Typical examples Find a and b Very angles often, the exam tries to confuse you by drawing the chords Imagine in the
Chord Angle have a = 44 to see the YOU Angles on the same chord for yourself Imagine the Chord Angle b = 28 Angle at the centre A
Consider the two angles which stand on this same chord What do you notice about the angle at the circumference? Chord It is half the angle at the centre We say If two angles stand on the same chord,
then the angle at the centre is twice the angle at the circumference Angle at the centre Its still true when we move The apex, A, around the circumference 272 A 136
As long as it stays in the same segment Of course, the reflex angle at the centre is twice the angle at circumference too!! We say If two angles stand on the same chord, then the angle at the centre is twice the angle at the circumference Angle at Centre A Special Case
a When the angle stands on the diameter, what is the size of angle a? The diameter is a straight line so the angle at the centre is 180 Angle a = 90 We say The angle in a semi-circle is a Right Angle A Cyclic Quadrilateral
is a Quadrilateral whose vertices lie on the circumference of a circle Opposite angles in a Cyclic Quadrilateral Add up to 180 They are supplementary We say Opposite angles in a cyclic quadrilateral add up to 180 Questions
Could you define a rule for this situation? Tangents When a tangent to a circle is drawn, the angles inside & outside the circle have several properties. 1. Tangent & Radius A tangent is perpendicular to the radius of a circle
2. Two tangents from a point outside circle Tangents are equal PA = PB PO bisects angle APB
Angle between tangent & chord We say The angle between a tangent and a chord is equal to any Angle in the alternate (opposite) segment
American Psychiatric Association DSM-III and Robert L. Custer, MD Brecksville VA Hospital - 1972 Custer conducted research on the patients Custer lobbied the American Psychiatric Association (DSM-III 1980) Pathological Gambling included under "Disorders of Impulse Control, NEC" along with kleptomania,...
Title: PowerPoint Presentation Last modified by: Gorku Sanchog Document presentation format: On-screen Show Other titles: Comic Sans MS Times Times New Roman Default Design Slide 1 Micronesian - Polynesian colonization of Pacific Ocean Islands Slide 3 Slide 4 Slide 5...
Your own organization's grapevine. ... Human activity: people define. Categorization schemes. Mediate between others with different views. Monitor capture process to see if new categories needed. Update categorization scheme frequently. Labor intensive to do it well.
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Idea needs more explanation or specificity; Represents literal reading of the text; No text evidence or flawed text evidence; Evidence generally references the text; Evidence too partial to support idea; Weak link to idea; Wrongly manipulates meaning of text; Evidence...
O come, all ye faithful, Joyful and triumphant,O come ye, O come ye, to Bethlehem.Come and behold Him, Born the King of angels. Jingle Bells [Refrain] O come, let us adore Him,O come, let us adore Him,O come, let us...
Indian achievements were passed to Arabs Colonies of Arabs settled along India's coasts, adopted local customs Provided staging points for Islamic expansion The Coming of Islam to South Asia 10th Century- a Turkish dynasty gained power in Afghanistan 12th Century-...
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