# construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. also to verify the measurement by actual calculation.

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## Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

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## Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

(1)Draw two concentric circle CEasy Open in App Solution Verified by Toppr 1 and C 2 with common center

0 and radius 4cm and 6cm

(2) Take a point P on the outer circle C

2 and join OP.

(3) Draw the bisector of OP which bisect OP at M'.

(4) Taking M' as center and OM' as radius draw a dotted circle which

cut the inner circle C

1

at two point M and P.

(5) Join PM and PP'. Thus, PM and PP' are required tangent.

On measuring PM and PP'.

PM=PP ′ =4.4cm Bycalculation: InΔOMP,∠PMO=90 0 PM 2 =OP 2 −OM 2

(bypythagorastheorem)

PM 2 =(6) 2 −(4) 2 =36−16=20 PM 2 =20cm PM= 20 =4.4cm Hence,

thelengthofthetangentis4.4cm

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## Construct a Tangent to a Circle of Radius 4 Cm Form a Point on the Concentric Circle of Radius 6 Cm and Measure Its Length. Also, Verify the Measurement by Actual Calculation.

Construct a Tangent to a Circle of Radius 4 Cm Form a Point on the Concentric Circle of Radius 6 Cm and Measure Its Length. Also, Verify the Measurement by Actual Calculation.

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Construct a tangent to a circle of radius 4 cm form a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm ?

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### SOLUTION 1

Steps of Construction

Step 1: Mark a point O on the paper

Step 2: With O as center and radii 4cm and 6cm, draw two concentric circles.

Step 3: Mark a point P on the outer circle.

Step 4: Join OP.

Step 5: Draw the perpendicular bisector XY of OP, cutting OP at Q.

Step 6: Draw a circle with Q as center and radius OQ (or PQ), to intersect the inner circle in points T and T’.

Step 7: Join PT and PT’.

Here, PT and PT’ are the required tangents.

PT = PT’ 4.5 cm (Approx)

Verification by actual calculation

Join OT to form a right ΔOTP (Radius is perpendicular to the tangent at the point of contact)

In right ΔOTP, OP2=OT2+PT2

(Pythagoras Theorem)

⇒PT=OP2-OT2

⇒PT=62-42=36-16=20 ≈ 4.5cm

(OP = 6 cm and OT = 4cm)

### SOLUTION 2

**Steps of construction:**

1. Draw two concentric circles with centre O and radii 4 cm and 6 cm. Take a point P on the outer circle and then join OP.

2. Draw the perpendicular bisector of OP. Let the bisector intersects OP at M.

3. With M as the centre and OM as the radius, draw a circle. Let it intersect the inner circle at A and B.

4. Join PA and PB. Therefore,

PA¯ and PB¯

are the required tangents.

Concept: Construction of Tangents to a Circle

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Chapter 13: Constructions

Q 10 Q 9

### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths

Chapter 13 Constructions

Q 10

2012-2013 (March) Delhi set 3 (with solutions)

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## Ex 11.2, 2

Ex 11.2, 2 Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation. Steps of construction Draw a circle of radius 4 cm with center O Draw concentric circle of radius 6 cm,

## Ex 11.2, 2 - Chapter 11 Class 10 Constructions (Term 2)

Last updated at July 14, 2020 by Teachoo

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