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
Solution:
Steps of construction:
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Take ‘O’ as centre and radius 4 cm and 6 cm respectively to draw two circles.
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Take a point ‘P’ on the bigger circle and join OP.
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With ‘O’ and ‘P’ as centre and radius more than half of OP draw arcs above and below OP to intersect at X and Y.
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Join XY to intersect OP at M.
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With M as centre and OM as radius draw a circle to cut the smaller circle at Q and R.
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Join PQ and PR. PQ and PR are the required tangents, where PQ = PR = 4.5 cm (approx.)
Proof:
∠PQO = 90º (Angle in a semi-circle)
∴ PQ ⊥ OQ
OQ is the radius of the smaller circle and PQ is the tangent at Q.
In the right ΔPQO,
OP = 6 cm (radius of the bigger circle)
OQ = 4 cm (radius of the smaller circle)
PQ² = (OP)² - (OQ)²
= (6)² - (4)²
= 36 - 16
= 20
PQ = √20
= 4.5 (approx)
Similarly, we can prove PR = 4.5 (approx.)
☛ Check: NCERT Solutions for Class 10 Maths Chapter 11
Video Solution:
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
NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 Question 2
Summary:
PR is the required tangent of 4.5 cm length constructed to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm. The measurement by actual calculation has been verified.
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