Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Define a tangent to a circle. A that touchesbisects the circle at exactly point(s).

(2) What is the angle between a tangent and the radius at the point of contact? °

Correct! The tangent is always perpendicular to the radius at the point of contact.

(3) How many tangents can be drawn from a point on the circle?

Perfect! Only one tangent can be drawn from any point on the circle.

(4) Write the relationship between the radius and the tangent of a circle. Radius is to the tangent of a circle.

(5) What is a secant of a circle? A that intersectstouches the circle at point(s).

Excellent! A secant cuts through the circle at two distinct points.

(6) What is the maximum number of tangents that can be drawn from a point outside a circle?

(7) Can a line be both a tangent and a secant? Why or why not? NoYes

They are mutually exclusiveinclusive.

Correct! A line cannot be both - it either touches at one point (tangent) or intersects at two points (secant).

Short Answer Questions (2 Marks Each)

(1) Prove that the tangents drawn to a circle from an external point are equal in length.

(2) Find the length of the tangent from a point 13 cm from the center of a circle of radius 5 cm. Length = cm

Perfect! Using Pythagoras theorem: tangent2 = distance2 - radius2 = 132 - 52 = 169 - 25 = 144, so tangent = 12 cm.

(3) Draw a rough diagram showing a circle, its center, and two tangents from a point outside the circle.

(4) Two tangents TP and TQ are drawn to a circle from an external point T. Show that ∠PTQ is bisected by the line joining T and the center of the circle.

(5) Find the distance from a point to the center of the circle if the radius is 6 cm and the length of the tangent is 8 cm. Distance = cm

Excellent! Using Pythagoras: distance2 = radius2 + tangent2 = 62 + 82 = 36 + 64 = 100, so distance = 10 cm.

(6) A circle has a radius of 7 cm. A tangent is drawn from a point P to the circle. If the distance from P to the center is 25 cm, find the length of the tangent. Length = cm

Perfect! tangent2 = 252 - 72 = 625 - 49 = 576, so tangent = 24 cm.

(7) Draw a circle and construct a tangent from a point outside the circle using ruler and compass.

(8) From a point 10 cm away from the center of a circle of radius 6 cm, find the length of the tangent. Length = cm

Great! tangent2 = 102 - 62 = 100 - 36 = 64, so tangent = 8 cm.

Long Answer Questions (4 Marks Each)

(1) Prove that the lengths of tangents drawn from an external point to a circle are equal. Use geometrical reasoning and construction.

(2) From a point 13 cm away from the center of a circle, a tangent of length 12 cm is drawn. Find the radius of the circle using the Pythagoras Theorem. Radius = cm

Perfect! radius2 = distance2 - tangent2 = 132 - 122 = 169 - 144 = 25, so radius = 5 cm.

(3) Draw a circle and construct two tangents from a point outside the circle. Prove that they are equal in length.

(4) A point P is 17 cm from the center of a circle. If the length of the tangent from P to the circle is 15 cm, find the radius of the circle. Radius = cm

Excellent! radius2 = 172 - 152 = 289 - 225 = 64, so radius = 8 cm.

(5) Prove that the angle between two tangents drawn from an external point is equal to the angle subtended by the line joining the center and the external point at the circle.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The tangent at any point of a circle is ? to the radius through the point of contact.

(a) Parallel (b) Perpendicular (c) Equal (d) Same

Correct! The tangent is always perpendicular to the radius at the point of contact.

(2) From an external point, how many tangents can be drawn to a circle?

(a) 1 (b) 2 (c) 3 (d) Infinite

Correct! Exactly two tangents can be drawn from any external point to a circle.

(3) The length of the tangent drawn from a point 5 cm away from the center of a circle of radius 3 cm is:

(a) 2 cm (b) 9 cm (c) 4 cm (d) 5 cm

Correct! Using Pythagoras: tangent2 = 52 - 32 = 25 - 9 = 16, so tangent = 16 = 4 cm.

(4) A secant intersects a circle in:

(a) One point (b) Two points (c) Three points (d) No point

Correct! A secant line intersects the circle at exactly two distinct points.

(5) The number of tangents that can be drawn to a circle from a point inside it is:

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

Correct! No tangents can be drawn from a point inside the circle.

(6) The point from which two tangents are drawn to a circle is called:

(a) Interior Point (b) Point of Contact (c) External Point (d) Center

Correct! The external point is outside the circle from which tangents are drawn.

(7) A line that touches a circle at more than one point is called a:

(a) Radius (b) Diameter (c) Secant (d) Tangent

Correct! A secant intersects the circle at two points, while a tangent touches at only one point.

(8) Which of the following statements is true?

(a) A secant touches the circle at only one point

(b) A radius is always longer than a tangent

(c) Tangents drawn from an external point are unequal

(d) Two tangents can be drawn from a point outside a circle

Correct! This is a fundamental property - exactly two tangents can be drawn from any external point.

Tangents and Secants Challenge

Determine whether these statements about tangents and secants are True or False:

Tangents and Secants Quiz