Everything Maths Grade 12

9.2 CHAPTER 9. GEOMETRY ABSˆ +ABTˆ = 90◦(TB⊥ SR) BATˆ = 90◦(∠s at centre) ∴ABTˆ +ATBˆ = 90◦(sum of angles in�BAT ) ∴ABSˆ = ATBˆ ...

CHAPTER 9. GEOMETRY 9.2 O P Q R S d c O P Q R S g P R 33 ◦ b a O P Q R S e h+50◦ 3 h 34 ◦ m O Q S 8 ◦ f O Q S 17 ◦ 52 ◦ k O Q S ...

9.2 CHAPTER 9. GEOMETRY More practice video solutions or help at http://www.everythingmaths.co.za (1.) 022a (2.) 022b (3.) 022c ...

CHAPTER 9. GEOMETRY 9.2 � A B O P R � A B O R P More practice video solutions or help at http://www.everythingmaths.co.za (1.) 0 ...

9.2 CHAPTER 9. GEOMETRY Prove that: CFOE is a cyclic quadrilateral FB = BC 3.�COE///�CBF CD^2 = ED×AD 5.OEBC=CDCO SOLUTION S ...

CHAPTER 9. GEOMETRY 9.2 In�EDC CEDˆ = 180◦−x (∠’s on a straight line AD) ECDˆ = 90◦−x (complementary∠’s) Step 5 : Now look at th ...

9.2 CHAPTER 9. GEOMETRY Example 2: Circle Geometry II QUESTION A B C D E F G H FD is drawn parallel to thetangent CB Prove that: ...

CHAPTER 9. GEOMETRY 9.2 Let∠FEA = y ∴∠FDA = y (∠’s subtended by same chord AF in cyclic quadrilateral FADE) ∴∠CBD = y (correspon ...

9.3 CHAPTER 9. GEOMETRY 9.3 Co-ordinate Geometry Equation of a Circle EMCBZ We know that every point on the circumferenceof a ci ...

CHAPTER 9. GEOMETRY 9.3 Example 3: Equation of a Circle I QUESTION Find the equation of a circle (centre O) with a diameter betw ...

9.3 CHAPTER 9. GEOMETRY The distance between the two points is: r = 1 2 PQ = 1 2 � (x 2 −x 1 )^2 + (y 2 −y 1 )^2 = 1 2 � (5− (−5 ...

CHAPTER 9. GEOMETRY 9.3 ∴ centre is (7;−2) and the radius is 5 units Equation of a Tangent toa Circle at a Point on the Circle E ...

9.3 CHAPTER 9. GEOMETRY Now, we know that thetangent passes through (x 1 ;y 1 ) so the equation is givenby: y−y 1 = mg(x−x 1 ) y ...

CHAPTER 9. GEOMETRY 9.4 (f) x^2 − 3 x + 9 = y^2 + 5y + 25 = 17 Find the x and y intercepts of the following graphs and draw a s ...

9.4 CHAPTER 9. GEOMETRY Polar co-ordinates � r y x α P Notice that sinα =yr∴ y = r sinα and cosα =xr∴ x = r cosα so P can be exp ...

CHAPTER 9. GEOMETRY 9.4 Any line OP is drawn (not necessarily in the first quadrant), making an angle of θ degrees with the x-ax ...

9.4 CHAPTER 9. GEOMETRY Description Transformation (translation, reflection, Co-ordinates Lengths Angles rotation, enlargement) ...

CHAPTER 9. GEOMETRY 9.4 (c) (x,y)→ (4x;y) (d) (x,y)→ (3x;y + 2) (e) (x,y)→ (−x;−y) (f) (x,y)→ (x;−y + 3) (g) (x,y)→ (4x; 4y) (h) ...

Trigonometry 10 11.1 Introduction EMCCE In this chapter we will build on the trigonometryfrom previous years by looking at the r ...

CHAPTER 10. TRIGONOMETRY 10.2 1 1 x y a b � � � (α−β) α β L(a;b) K(x;y) O M (x;y) We can get the coordinates of L and K in terms ...