Maths Worksheet - Geometry

SAEP Matric Success – Zisukhanyo Maths Worksheet Tuesday 28th April 2009 Geometry 1. Determine the values of the letters. O is the centre of the circle.

2. Determine the values of the letters. O is the centre of the circle.

3. Determine the values of the letters. O is the centre of the circle and BA is a tangent.

4. TOMX is a diameter of the circle with centre O and chord BC = 30 cm. If TOMX ┴ BC and OM = 2MX, calculate TB (to one d.p.)with reasons.

5. In the figure O is the centre of the circle; AB = BC and angle C = x. a) Determine angle ABO in terms of x. b) Prove that OB bisects angle ABC c) if OT : TB = 1 : 3 and OA = r, determine AC in terms of r.

6. AB is the diameter of a circle with centre P. Chord CD is perpendicular to AB and cuts AB in O. Chord DE cuts AB in F. CE, CB, DB, PC and AC are drawn. Prove that: a) angle CBO = angle DBO b) angle CED = 2 x angle CBP c) CEFP is a cyclic quadrilateral

7. In the figure A(3 ; -8) and B(9 ; 10) are two vertices of triangle ABC. The altitude AD cuts the median CM at Q(9 ; 4). Determine: a) the gradient of AQ b) the equation of BC c) the equation of CM d) angle BAQ

8. Determine the length of a tangent drawn from the point (6 ; -2) to the circle x2 + y2 -6x + 2y + 8 = 0. 9. A circle with centre M(5 ;4) and radius 5 cuts the x-axis at A and B, with A the point closest to the origin. a) Write down the equation of the circle b) Find the co-ordinates of A and B c) Determine the equations of the tangents to the circle from a point P with points of contact A and B. d) Determine the co-ordinates of P. e) Determine the co-ordinates of the centre of a circumscribed circle of quadrilateral AMBD f) Calculate the size of angle AMB