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  1. Chapter 11 Class 10 Constructions
  2. Serial order wise
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Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. The tangents can be constructed on the given circles as follows. Draw a line segment AB of 8 cm. Taking A and B as centre, draw two circles of 4 cm and 3 cm radius. Bisect the line AB. Let the mid-point of AB be C. Taking C as centre, AC as radius, draw a circle which intersects the circles at points P, Q, R, and S. Join BP, BQ, AS, and AR. These are the required tangents. Justification: We need to prove BP and BQ are tangents to larger circle. AS and AR are tangents to smaller circle. Join BS and BR. ∠ASB is an angle in the semi-circle of the blue circle And we know that angle in a  semi-circle is a right angle. ∴ ∠ASB = 90° ⇒ AS ⊥ BS Since BS is the radius of the circle, AS has to be a tangent of the circle. Similarly, AR, BP, BQ are tangents.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.