Unit Test: Circles

Q1: A circle has a number of tangents equal to (1 Mark)

(a) 0
(b) 1
(c) 2
(d) Infinite

Q2: If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is: (1 Mark)

(a) 90º
(b) 50º
(c) 70º
(c) 40º

Q3: If a parallelogram circumscribes a circle, then it is a ______________________.

Q4: Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is:

(a) 8 cm
(b) 10 cm
(c) 12 cm
(d) 18 cm

Q5: What is a secant? (1 Mark)

Q6: If PS and PT are tangents from an external point P such that PS = 10 cm and ∠SPT = 60°. Find the length of chord ST. (2 Marks)

Q7: In the given figure, O is the centre of the circle, PT is the tangent and PAB is the secant passing through centre O. If PT = 8 cm and PA = 4 cm, then find the radius of the circle. (2 Marks)

Q8: A circle touches the side BC of a ∆ABC at P, and touches AB and AC produced at Q and R respectively as shown in fig. Show that AQ = 1/2 (Perimeter of ∆ABC).  (2 Marks)

Q9: In figure, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and ∠APB = 60° Find the length of chord AB.  (3 Marks) 

Q10: ABC is a right-angled triangle, right angled at B and with BC = 6 cm and AB = 8 cm. A circle with centre O and radius x has been described in AABC. Find the values of x. (3 Marks)

Q11: In figure, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle. (3 Marks)

Q12: In the adj oining figure from an external point P, a tangent PT and a line segment PAB is drawn to a circle with centre O. ON is perpendicular on the chord AB. Prove that (5 Marks)
(i) PA.PB = PN² - AN²
(ii) PN² - AN² = OP² - OT²
(iii) PA.PB = PT²

Q13: From point P outside the circle, with centre O, tangents PA and PB are drawn in the adjoining fig. If OP is equal to the diameter of the circle, prove that PAB is an equilateral triangle. (5 Marks)

You can find the solutions of this Unit Test here: Unit Test (Solutions): Circles