Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation
Solution:
Steps of Construction
1. Construct two concentric circles of radii 3 cm and 5 cm
2. Consider a point P on the outer circle. The distance of point P from O is 5 cm
3. Let us bisect the line segment OP and consider it as M
4. Taking M as centre and PM as radius construct a circle. Let this circle intersect the circle with radius 3 cm at the points T and T’
5. Now join PT and PT’. They are the required tangents to the inner circle.
6. 3 cm is the radius of inner circle and 5 cm is the distance of point P from O
7. From the Pythagoras theorem, the length of tangent is 4 cm.
OP = 5 cm
OT = 3 cm
OP² = OT² + PT²
5² = 3² + PT²
PT² = 25 - 9
PT² = 16
So we get
PT = 4 cm
Therefore, the length of the tangent is 4 cm.
✦ Try This: Draw two concentric circles of radii 2 cm and 3 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11
NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 3
Draw two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation
Summary:
Two concentric circles of radii 3 cm and 5 cm are drawn. Taking a point on outer circle the pair of tangents to the other are constructed. The length of the tangent is 4 cm
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