Download presentation

Presentation is loading. Please wait.

1
**Proofs for circle theorems**

Tuesday, 13 July 2010

2
**1. Angle subtended at the centre**

The angle subtended at the centre from an arc is double the angle at the circumference. y x 180 – 2x C x B 180 – 2y 2x+2y = 2(x+y) y A

3
**2. Angles subtended from the same arc.**

Angles subtended from the same arc are equal. C B A

4
**3. Angles in a semi-circle.**

The largest angle in a semi-circle will always be 90 90 C A B

5
**4. The Angle between a Tangent and its radius.**

Definition: A tangent is a line that will touch the circle at one point only. (i.e. it does not cut the circle) C Tangent Assume that the tangent is not perpendicular to the radius. Now there must be a perpendicular from the center of the circle to the tangent. It must intersect the tangent elsewhere (apart from the point on intersection). Now since a perpendicular is the shortest distance of a point from a line, the perpendicular must have distance < radius of the circle (since line from point of intersection of tangent to center of circle is a radius). => the foot of the perpendicular must lie within the circle. =>the line meets the circle elsewhere and the line is not really a tangent! Thus there is a contradiction. Therefore the radius is the shortest distance. Consequently, it must be perpendicular to the tangent at the point of intersection 90 A The angle between a tangent an its radius will always be 90

6
**5. Angles in a cyclic quadrilateral.**

Definition: A cyclic quadrilateral is any four-sided polygon whose four corners touch the circumference of the circle 180 – d b 2 360 –2 Opposite angles in a cyclic quadrilateral add up to 180 c

7
**4. The Angle between a Tangent and a chord.**

Definition: A chord is any straight line which touches the circumference at two points. The largest chord possible is called the diameter. =180 – 90 – (90 – ) = Tangent 90 90 – Chord The angle between a tangent a chord is equal to the angle in the alternate segment.

Similar presentations

Presentation is loading. Please wait....

OK

Mr Barton’s Maths Notes

Mr Barton’s Maths Notes

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on construction maths for class 10th Ppt on data handling for grade 3 Ppt on windows 7 operating system Ppt on electricity for class 10th sample Ppt on producers consumers and decomposers poem Ppt on nitrogen cycle and nitrogen fixation process Ppt on personal grooming and etiquette Ppt on number system for class 9 free download Ppt on rain water conservation Ppt on summary writing guidelines