Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents
Solution:
Steps of construction:
1. Construct a circle with O as centre and 4 cm radius
2. Construct any diameter AOB
3. Construct an angle ∠AOP = 60º where OP is the radius which intersect the circle at the point P
4. Construct PQ perpendicular to OP and BE perpendicular to OB
PQ and BE intersect at the point R
5. RP and RB are the required tangents
6. The measurement of OR is 8 cm
Justification:
PR is the tangent to a circle
∠OPQ = 90º
BR is the tangent to a circle
∠OBR = 90º
So we get
∠POB = 180 - 60 = 120º
In BOPR
∠BRP = 360 - (120 + 90 + 90) = 60º
Therefore, the distance between the centre of the circle and the point of intersection of tangents is 8 cm.
✦ Try This: Draw a circle of radius 5 cm. Construct a pair of tangents to it, the angle between which is 30º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11
NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 6
Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents
Summary:
A circle of radius 4 cm is drawn. A pair of tangents is constructed where the angle between which is 60º. The measurement of the distance between the centre of the circle and the point of intersection of tangents is 8 cm
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