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  1. Chapter 11 Class 10 Constructions
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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. Tangents on the given circle can be drawn as follows. Draw a circle of 4 cm radius with centre as O on the given plane. Draw a circle of 6 cm radius taking O as its centre. Locate a point P on this circle and join OP. Bisect OP. Let M be the mid-point of OP Take M as its centre and MO as its radius, draw a circle. Let it intersect the given circle at the points Q and R. Join PQ and PR. PQ and PR are the required tangents. By measuring, Lengths of PQ and PR is 4.47 m Finding lengths of PQ and PR Join OQ and OR Since tangent is perpendicular to radius PQO = 90 and PRO = 90 Thus, PQO is a right angled triangle, Also, PO = radius of bigger circle = 6 cm and OQ = radius of smaller circle = 4 cm By Pythagoras theorem PO2 = PQ2 + OQ2 62 = PQ2 + 42 36 = PQ2 + 16 PQ2 = 36 16 PQ2 = 20 PQ = 20 = (5 4) = 4 5 = 2 5 PQ = 2 2.236 PQ = 4.47 cm Similarly, PR = 4.47 cm Justification: We need to prove that PQ and PR are the tangents to the circle. Join OQ and OR. PQO is an angle in the semi-circle of the blue circle And we know that angle in a semi-circle is a right angle. PQO = 90 OQ PQ Since OQ is the radius of the circle, PQ has to be a tangent of the circle. Similarly, PR is a tangent of the circle.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.