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  1. Chapter 11 Class 10 Constructions
  2. Serial order wise
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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, Δ 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 provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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