Compassvale Sec Circle Properties Revision

1 COMPASSVALE SECONDARY SCHOOL MATHEMATICS DEPARTMENT 2022 SECONDARY 4E5N Practice Circles – Singapore Schools Exam Papers Name: _______________________________( ) Class: __________ Marks: Date: _____________ Question 1 The perpendicular bisector of a chord, RS, cuts it at T and the circumference of the circle at P. If RS = 20 cm and TP = 8 cm, find the radius of the circle. Question 2 In the diagram below, A, C, D and F lie on a circle with centre O. Line OB is perpendicular to chord AC and E is the mid-point of chord DF. Given that AC = 6 cm, DF = 10 cm, OE = 5 cm and OB = y cm, find the value of y correct to 3 significant figures. A C D E F O B 6 cm 10 cm 5 cm y cm 50 20 cm R S O T P 8 cm

2 Question 3 In the diagram, A, B, C and D lie on the circumference of a circle. The straight lines AC and BD intersect at X. AB = 4 cm, BX = 2 cm and CD = 9 cm. (a) Prove that triangles ABX and CDX are similar. (b) Calculate the length of CX. (c) Calculate the ratio of area of triangle ABX : area of triangle DCX. Question 4 The diagram shows a circle with centre O. AC is a tangent to the circle. AOF, FDB and ODC are straight lines. Given that  46 and 24 HAFACO . (a) Write down why  90FAB . A B C D X 2 4 9 A B C D E F G H O 46 24

3 (b) Calculate (i) HEF . (ii) AFB . (iii) HGF . (iv) FED . Question 5 In the diagram, AC is a diameter of the circle with center O. The chords AE and BC meet at D when produced. Given that  22CDE and  39BAC . Find (a) ACB , (b) AEB , (c) CBE . Question 6 The points A, B, C, D and E lie on a circle, centre O. AD is a diameter of the circle. BQ is a tangent to the circle,  24AEB and QAD is a straight line. Calculate, stating your reasons clearly, (a) (i) BAD . (ii) BED . (iii) BQA . (iv) reflex BOD . (v) ABQ . (b) If  xDAE , show that  )114( xQBE . Q B C D E A O 24 D A B O E C 22 39

4 (c) Given that  43ABE , determine whether the lines BO and AE are parallel. Give a reason for your answer. Question 7 In the diagram, AC is a diameter of the circle ABCDE. AC and ED are extended to meet at F. Given that CE = CF,  xAFD and  yBED . (a) Explain with reasons why  xDBC . (b) Find, in terms of x and/or y, (i) ACD . (ii) ACE . (iii) BCD . Question 8 In the figure below, PQRST is a circle with O as the centre. PX and RX are tangents to the circle at points P and R respectively. Given that  40 and 78 SPQPXR , calculate (a) PRX . (b) POR . (c) OST . (d) QRX . T P O S R Q X 40 78

5 Question 9 A, B, C, D and E lie on a circle. AC is a diamete