NCERT Class 10 Maths Lab Manual – Tangents drawn from an External Point

NCERT Class 10 Maths Lab Manual – Tangents drawn from an External Point

Objective
To verify experimentally that lengths of tangents drawn from an external point to a circle are equal.

Tangent
A line touchingthe circle at a point is called a tangent to the circle.

Prerequisite Knowledge

1. Tangent to a circle.
2. Length of a tangent.
   

Materials Required
Glazed papers, a white chart paper, sketch pens, a pair of scissors, geometry box, fevicol.

Procedure

1. Cut a circle of any radius from a glazed paper and paste it on a white chart paper.
   
2. Take any point P on the circle.
   
3. From P, fold the paper in such a way that it just touches the circle at P. Press it and unfold to get a tangent PA.
   
4. From A, fold the paper to get tangent AQ.
   
5. Fold the circle along OA.
6. Join OP, OA, OQ.
   

Observation
Students observe that point P coincide with Q
∴ AP = AQ

Result
Thus it is verified that lengths of tangents drawn from an external point to a circle are equal.

Learning Outcome
Students will learn how to measure tangents from an external point to a circle by using paper folding.

Activity Time

1. Draw two tangents from a point P to a circle of radius 3 cm. If its distance from the centre is 10 cm, measure the lengths of the tangents. Are they equal ?
2. In the adjoining figure, prove that AD+BC = AB+CD
   
3. In the adjoining figure, find PQ and PR.
   

Viva Voce

Question 1.
Define tangent to a circle.
Answer:
A line touching the circle at one point is called a tangent to that circle.

Question 2.
Is it possible that a line can touch the circle at more than one point ?
Answer:
No

Question 3.
How many tangents can be drawn to a circle from a common point outside the circle ?
Answer:
Two

Question 4.
Is it possible to draw a tangent from a point inside the circle ?
Answer:
No

Question 5.
Is it possible to draw two tangents of different lengths from a common external point ?
Answer:
No

Question 6.
In the fig. (i), is ∆POQ ≅ ∆POR?

Answer:
Yes.

Question 7.
Is a tangent at any point of a circle perpendicular to the radius through the point of contact ?
Answer:
Yes.

Question 8.
In the fig. (i), is √x = √y ?
Answer:
Yes

Multiple Choice Questions

Question 1.
The distance between two parallel tangents drawn to a circle is equal to the
(a) diameter of circle
(b) radius of circle
(c) twice of diameter
(d) none of these

Question 2.
At the point of contact, the angle between radius and tangent to a circle is
(a) 180°
(b) 90°
(c) acute angle
(d) none of these

Question 3.
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ= 12 cm. Length of PQ is
(a) 12 cm
(b) 13 cm
(c) 8.5 cm
(d) √119 cm

Question 4.
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
(a) 7 cm
(b) 12 cm
(c) 15 cm
(d) 24.5 cm

Question 5.
TP and TQ are two tangents to a circle with centre O, so that ∠POQ = 110°, then ∠PTQ is equal to
(a) 60°
(b) 70°
(c) 80°
(d) 90°

Question 6.
If tangent PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80°, then ∠POA is equal to
(a) 50°
(b) 60°
(c) 70°
(d) 80°

Question 7.
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) 5 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm

Question 8.
In the figure, If PQ = PR, then which is correct

(a) QS = SR
(b) QS = 2RS
(c) QS ≠ RS
(d) none of these

Question 9.
AB and AC are two tangents drawn to the circle with centre O. If ∠BAC = 85° then ∠BOC is
(a) 95°
(b) 85°
(c) 90°
(d) 80°

Question 10.
PQ and PR are tangents from point P to the circle with centre O. N is a point on the circle, then choose the correct-relation

(a) PL + MN = PM – LN
(b) PL + MN = PM + LN
(c) PL + PM = LN + MN
(d) PL + LN = PM + MN

Answers

1. (a)
2. (b)
3. (d)
4. (a)
5. (b)
6. (a)
7. (d)
8. (a)
9. (a)
10. (d)

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