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Ex 11.2, 4 - Draw pair of tangents to a circle of radius 5 cm inclined

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

 

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Ex 11.2, 4 (Concept) Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°. Given angle between tangents is 60° i.e. ∠ QPR = 60° Since Angle at center is double the angle between tangents ∴ ∠ OQR = 2 × 60° = 120° So, we need to draw ∠ QOR = 120° ∴ We draw a radius, then second radius at 120° from first. Also, Tangent is perpendicular to radius So, OQ ⊥ QP & OR ⊥ PR Thus, to make tangents, we draw perpendicular from point Q and R So, we draw 90° from point Q and point R Thus, our figure will look like Ex 11.2, 4 Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°. Steps of construction Draw a circle of radius 5 cm Draw horizontal radius OQ 3. Draw angle 120° from point O Let the ray of angle intersect the circle at point R Now, draw 90° from point Q 5. Draw 90° from point R 6. Where the two arcs intersect, mark it as point P ∴ PQ and PR are the tangents at an angle of 60° Justification We need to prove that PQ and PR are the tangents to the circle at angle of 60° . Since ∠ PQO = 90° ∴ PQ ⊥ QO Since tangent is perpendicular to radius, and QO is the radius ∴ PQ is the tangent to the circle Similarly, PR is the tangent to the circle Now, we prove ∠ P = 60° In quadrilateral PQOR Sum of angles = 360° ∠ P + ∠ Q + ∠ R + ∠ QOR = 360° ∠ P + 90° + 90° + 120° = 360° ∠ P + 180° + 120° = 360° ∠ P + 300° = 360° ∠ P = 360° – 300° ∠ P = 60° So, PQ and PR are tangents at an angle of 60°

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.