Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 2
105 practice questions
Topics covered
Practice questions
61–70 of 105
Question 61
2 marks · Normal
Answer and see the solution →Find the length of the side marked x in this right-angled triangle.
(a)[2 marks]Question 62
1 mark · Normal
Answer and see the solution →Write down the name given to a straight line that touches a circle at only one point.
(a)[1 mark]Question 63
3 marks · Normal
Answer and see the solution →A, B, C, and D lie on a circle with centre O. Angle ABC is 115°.
Diagram not accurately drawn. (a)[2 marks]Work out the size of angle CDA.
(b)[1 mark]Explain why your answer is correct.
Question 64
4 marks · Normal
Answer and see the solution →The diagram shows a circle with centre O. The radius of the circle is 5 cm. Chord AB is 8 cm long.
(a)[3 marks]Find the perpendicular distance from O to AB.
(b)[1 mark]Explain why this line bisects AB.
Question 65
4 marks · Normal
Answer and see the solution →In the circle below, centre O, angle BAC = 70° and chord BC is a diameter.
(a)[2 marks]Calculate angle ABC.
(b)[2 marks]Give a reason for your answer.
Question 66
4 marks · Normal
Answer and see the solution →The diagram shows a circle with centre O. PT is a tangent to the circle at P. OP = 7 cm. Work out the length OT if angle OPT = 60°.
Circle with tangent and radius. (a)[3 marks]Find OT.
(b)[1 mark]State the property relating the tangent to the radius at P.
Question 67
2 marks · Normal
Answer and see the solution →A square has sides of length 6 cm. Calculate the length of its diagonal to 3 significant figures.
(a)[2 marks]Question 68
4 marks · Hard
Answer and see the solution →In the diagram below, ABCD is a cyclic quadrilateral inside a circle with centre O.
Cyclic quadrilateral with angles marked. Angle BAD = 82° and angle BCD = 71°.
Calculate the size of angle ABC, giving a reason for each step of your working.
Question 69
4 marks · Hard
Answer and see the solution →The diagram below shows a circle with centre O. The point M is the midpoint of chord AB. AB = 14 cm and OM = 6 cm.
Circle with OM perpendicular to chord AB. Work out the radius of the circle.
Question 70
5 marks · Hard
Answer and see the solution →The diagram below shows a tangent to the circle with centre O. P is the point of contact, and the radius OP is 8 cm. The tangent TP meets a straight line passing through the centre O at point T, such that angle OTP = 35°.
Circle with tangent, radius, and angle marked. (a)[1 mark]State the relationship between the tangent and the radius at point P.
(b)[4 marks]Calculate the length TP. Give your answer to 3 significant figures.