Hint: Draw, identify and differentiate between secant and tangent of a circle in order to prove and apply various theorems related to circles.
Question.1. A figure is shown below. 
(a) Lines AG and CL are the tangents and line EF is a secant to the circle.
(b) Lines AG and CL are the secants and line EF is a tangent to the circle.
(c) Line AG is a tangent and lines EF and CL are the secants to the circle.
(d) Line AG is a secant and lines EF and CL are the tangents to the circle.
Question.2. A circle passes through point P. How many tangents and secants to the circle are possible that pass through P?
(a) Tangent: 1; Secant: 1
(b) Tangent: Infinite; Secant: 1
(c) Tangent: 1; Secant: Infinite
(d) Tangent: Infinite; Secant: Infinite
Ans.1. (a) Lines AG and CL are the tangents and line EF is a secant to the circle.
Ans.2. (c) Tangent: 1; Secant: Infinite
Hint: Prove and apply theorems related to tangent of a circle in order to determine number of tangents from the given point(s).
Question.3. A circle with centre O is shown below.
(a) There can be only one line passing through point T such that it is parallel to OT.
(b) There can be only one line passing through point T such that it is perpendicular to OT.
(c) There can be any number of lines passing through point T such that they are parallel to OT.
(d) There can be any number of lines passing through point T such that they are perpendicular to OT.
Question.4. A circle is shown below.
Statement II: The shortest distance of a tangent passing through point L from the centre O is equal to the radius of the circle, OL.
Statement III: One tangent can pass through two points K and L of a circle.
Which statement(s) is/are correct?
(a) Statement I and II
(b) Statement I and III
(c) Statement II and III
(d) Statement I, II and III
Ans.3. (b) There can be only one line passing through point T such that it is perpendicular to OT.
Ans.4. (a) Statement I and II
Hint: Prove and apply theorem related to tangent of a circle in order to determine length of the tangent.
Question.5. In the figure shown, RJ and RL are tangents of the circle. 
(a) 90° − 42°
(b) 90° − 84°
(c) 180° − 42°
(d) 180° − 84°
Question.6. In figure is shown, AC and BC are two tangents to the circle O with radius 5 cm.
(a) 24 cm
(b) 30 cm
(c) 32 cm
(d) 34 cm
Ans.5. (d) 180° − 84°
Ans.6. (c) 32 cm