Cambridge International Mathematics

Part 3: Radius-tangent theorem What to do: 1 Use a compass to draw a circle with centre O, and mark on it a point A. 2 Draw at A ...

Name of theorem Statement Diagram Radius-tangent The tangent to a circle is perpendicular to the radius at the point of contact. ...

de f g XY and YZ are tangents from point Y hi 2 A circle is drawn and four tangents to it are constructed as shown. Deduce that ...

7 In this question we prove thetangents from an external point theorem. a Join OP, OA and OB. b Assuming thetangent-radiustheore ...

A B D C O Part 2: Angles subtended by the same arc theorem What to do: 1 Use a compass to draw a circle with centre O. Mark on i ...

Example 2 Self Tutor Solve forx: ab a Obtuse AOBb = 360o¡ 250 o fangles at a pointg ) AOBb = 110o ) 2 x= 110 fangle at the centr ...

gh i 3 C is the point of contact of tangent CT. Findx, giving reasons for your answer. Hint: Draw diameter CD and join DB. 4 In ...

A circle can always be drawn through any three points that are not collinear. To find the circle’s centre we draw the perpendicu ...

Proof: Opposite angles of a cyclic quadrilateral Join OA and OC. Let ADCb =®o and AbBC= ̄o ) AOCb =2®o fangle at the centreg and ...

Example 4 Self Tutor x=80and y= 120 fexterior angles of a cyclic quadrilateralg EXERCISE 27B.1 1 Findxgiving reasons: abc de f 2 ...

3 ABCD is a cyclic quadrilateral. Sides AB and DC areproducedor extended to meet at E. Sides DA and CB are produced to F. If ang ...

Example 5 Self Tutor Triangle ABC is isosceles with AB=AC. X and Y lie on AB and AC respectively such that XY is parallel to BC. ...

4 A circle has centre O. The tangents to the circle from an external point P meet the circle at points A and B. Show that PAOB i ...

3 Find: a the length of side AB b the length of the radius of the circle. 4 AB and CM are common tangents to two circles. Show t ...

A B C D a° O b° 2 Copy and complete: Obtuse DbOB=:::::: f::::::g Likewise, reflex DbOB=:::::: f:::::::g ) ::::::+::::::= 360o fa ...

Challenge #endboxedheading 564 Circle geometry (Chapter 27) 1 A solid bar AB moves so that A remains on thex-axis and B remains ...

28 Contents: A Rational exponents [1.9, 2.4] B Exponential functions [3.2, 3.3, 3.5, 3.8] C Exponential equations [2.11] D Probl ...

InChapter 6we saw the followingexponent lawswhich are true for all positive basesaandband all integer indicesmandn. ² am£an=am+n ...

What to do: 1 Use the graphing package to draw the graphs of y=8x and x=^23 on the same set of axes. Find the value of 8 (^23) b ...

Consider a population of 100 mice which is growing under plague conditions. If the mouse population doubles each week, we can co ...