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Question
Draw a line segment OA , 5 cm long. AT O , using ruler and compasses only, construct OB such that , ∠ AOB = 37.5° construct a circle to touch OA at A and to touch OB at B.
Solution
Steps of construction :
(i) A 30 degree angle van be formed by knowing that the inverse sine of 0.5 is 30 degrees . In other words , a right triangle with a 30 degree angle has the hypotenuse twice as long as the leg opposite the near leg.
(ii) Using your compass, construct a 90° , then construct the leg opposite the 30 degree angle. Construct the hypotenuse twice as long , that makes a 30 degree angle.
(iii) Bisect 3 degree angle and you have 15 degrees,
(iv) From 90° cut off angle equal to 15° angle to get 75° angle. Bisect the 75° angle to get 37.5° angle.
(v) Now draw angle bisector of angle 37.5°.
(vi) On OR at 5 cm from O , drop a perpendicular PA from he angle bisector of angle 37.5°.
(vii) With PA as radius , draw a circle touching OA at A and OB at B.
This is the reqiured circle.
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