**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**

- Tangent to a circle.
- Length of a tangent.

**Materials Required**

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

**Procedure**

- Cut a circle of any radius from a glazed paper and paste it on a white chart paper.

- Take any point P on the circle.

- 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.

- From A, fold the paper to get tangent AQ.

- Fold the circle along OA.
- 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**

- 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 ?
- In the adjoining figure, prove that AD+BC = AB+CD

- 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**

- (a)
- (b)
- (d)
- (a)
- (b)
- (a)
- (d)
- (a)
- (a)
- (d)

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