Ex 11.2, 5 - Draw a line segment AB of length 8 cm. Taking A as centre

Ex 11.2, 5 - Chapter 11 Class 10 Constructions - Part 2
Ex 11.2, 5 - Chapter 11 Class 10 Constructions - Part 3 Ex 11.2, 5 - Chapter 11 Class 10 Constructions - Part 4 Ex 11.2, 5 - Chapter 11 Class 10 Constructions - Part 5 Ex 11.2, 5 - Chapter 11 Class 10 Constructions - Part 6

 

 

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Transcript

Question 5 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. Steps of construction Draw line segment AB of length 8 cm Taking A as center, draw a circle of radius 4 cm Taking B as center, draw a circle of radius 3 cm Now, we need to draw tangent from point A to the right circle, and from point B to the left circle. To draw tangents to the right circle, we need to draw perpendicular bisector of line AB 4. Make perpendicular bisector of AB Let M be the midpoint of AB. 5. Taking M as center and MA as radius, draw a circle. 6. Let blue circle intersect left circle at P, Q Let blue circle intersect right circle at R, S Join BP, BQ, AR and AS ∴ AR, AS and BP, BQ are the required tangents Justification We need to prove that BP, BQ, AR, AS are the tangents to the circle. Join OP, OQ, OR and OS Now, ∠APB is an angle in the semi-circle of the blue circle And we know that, Angle in a semi-circle is a right angle. ∴ ∠ABP = 90° ⇒ AP ⊥ BP Since AP is the radius of the circle, BP has to be a tangent of the circle. Similarly, we can prove BQ, AR, AS are tangents of the circle.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.