Circles

Topics in this chapter

• Circle Basics and Chord Properties
• Tangent Properties and Perpendicularity
• Tangent Lengths from External Points
• Common, Parallel, and Multiple Tangents
• Inscribed and Circumscribed Figures
• Intersecting and Concentric Circles
• Circle Area and Triangle Applications

Cheat sheet

Practice questions

1. Question 1Q-BD7C7C

   If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of $80^{\circ}$, then $\angle POA$ is equal to:

   1. A.$50^{\circ}$
   2. B.$60^{\circ}$
   3. C.$70^{\circ}$
   4. D.$80^{\circ}$
   See the answer and solution
2. Question 2Q-9A1C05

   From a point Q, the length of the tangent to a circle is $24$ cm and the distance of Q from the centre is $25$ cm. The radius of the circle is:

   1. A.$7$ cm
   2. B.$12$ cm
   3. C.$15$ cm
   4. D.$24.5$ cm
   See the answer and solution
3. Question 3Q-1E1E7A

   If TP and TQ are the two tangents to a circle with centre O so that $\angle POQ = 110^{\circ}$, then $\angle PTQ$ is equal to:

   1. A.$60^{\circ}$
   2. B.$70^{\circ}$
   3. C.$80^{\circ}$
   4. D.$90^{\circ}$
   See the answer and solution
4. Question 4Q-CDE895

   A quadrilateral ABCD is drawn to circumscribe a circle. If AB = $6$ cm, BC = $7$ cm, and CD = $4$ cm, then the length of AD is:

   1. A.$2$ cm
   2. B.$3$ cm
   3. C.$4$ cm
   4. D.$5$ cm
   See the answer and solution
5. Question 5Q-0AC8E4

   The maximum number of parallel tangents a circle can have on a given tangent line is:

   1. A.1
   2. B.2
   3. C.infinite
   4. D.0
   See the answer and solution