NCERT Solutions 11th Maths Chapter 11 Constructions Exercise 11.2

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Exercise 11.2
1. Draw a circle of radius 6 cm. From a point 10 cm away from its center, construct the pair of tangents to the circle and measure their lengths.
Solution:
Steps of Construction:
1. Draw a circle with center and radices = 6 cm.
2. Take a point P such that OP = 10 cm.
3. Draw the perpendicular bisector of OP. Let M is the mid-point of OP.
4. With center M and radius PM = MO, draw a circle which cuts the given circle at S and T.
5. Join PS and PT.
Thus, PS and PT are the required tangents.
The length of tangents Ps= PT = 8 cm.

Justification:

2.Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.
Solution:
Steps of Construction:
1. Draw two given concentric circles of radii 4 cm and 6 cm with common center O.
2. Take a point P on the circumference of a bigger circle and join OP
3. Mark the mid-point M of OP by drawing perpendicular bisector of it.
4. With center Mand radius MP = OM. draw a circle which intersects the smaller circle at S and T.
5. Join PS and PT.
Thus, PS and PT are the required tangents to the smaller circle.
On measuring PS = PT = 4.4 cm (app.)

Justification:
Join OS. In ∆PSO, ∠PSO = 90°