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| 1. |
Draw a circle of radius 5cm which are inclined to each other at angle 60° |
| Answer» The tangents can be constructed in the following manner:Step 1Draw a circle of radius 5 cm and with centre as O.Step 2Take a point A on the circumference of the circle and join OA. Draw a perpendicular to OA at point A.Step 3Draw a radius OB, making an angle of 120° (180° − 60°) with OA.Step 4Draw a perpendicular to OB at point B. Let both the perpendiculars intersect at point P. PA and PB are the required tangents at an angle of 60°.JustificationThe construction can be justified by proving that ∠APB = 60°By our construction∠OAP = 90°∠OBP = 90°And ∠AOB = 120°We know that the sum of all interior angles of a quadrilateral = 360°∠OAP + ∠AOB + ∠OBP + ∠APB = 360°90° + 120° + 90° + ∠APB = 360°∠APB = 60°This justifies the construction. | |