You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.
You are given a circle with radius 'r' and centre O. You are asked to draw a pair of tangents which are inclined at an angle of 60° with each other, from a point E. Refer to the figure and select the option which would lead us to the required construction. 'd' is the distance OE.
Construct the 
MNO as it is equilateral
Mark M and N on the circle such that 
MOE = 
and 
NOE = 
The correct option is C Mark M and N on the circle such that MOE = and NOE =
Since the angle between the tangents is 60° and OE bisects ∠MEN, ∠MEO = 30°. Now, since ΔOME is a right angled triangle, right angled at M, we realise that the ∠MOE = 60°. Since ∠MOE = 60°, we must have ∠NOE = 60° and hence ∠MON = 120°. Hence ΔMNO is NOT equilateral.
Since E is outside the circle, d can not be equal to r.
Recalling that ∠MOE = 60°, following are the steps of construction:
1. Draw a ray from the centre O.
2. With O as centre, construct ∠MOE = 60° [constructing angle 60° is easy]
3. Now extend OM and from M, draw a line perpendicular to OM. This intersects the ray at E. This is the point from where the tangents should be drawn, EM is one tangent.
4. Similarly, EN is another tangent.
Mark M and N on the circle such that MOE = and NOE =
Since the angle between the tangents is 60° and OE bisects ∠MEN, ∠MEO = 30°. Now, since ΔOME is a right angled triangle, right angled at M, we realise that the ∠MOE = 60°. Since ∠MOE = 60°, we must have ∠NOE = 60° and hence ∠MON = 120°. Hence ΔMNO is NOT equilateral.
Since E is outside the circle, d can not be equal to r.
Recalling that ∠MOE = 60°, following are the steps of construction:
1. Draw a ray from the centre O.
2. With O as centre, construct ∠MOE = 60° [constructing angle 60° is easy]
3. Now extend OM and from M, draw a line perpendicular to OM. This intersects the ray at E. This is the point from where the tangents should be drawn, EM is one tangent.
4. Similarly, EN is another tangent.
