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.

Answer 1

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.