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Question
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
Given, two concentric circles of radii 3 cm and 5 cm with centre O. We have to draw pair of tangents from point P on outer circle to the other.
Steps of construction:
- Draw two concentric circles with centre O and radii 3 cm and 5 cm.
- Taking any point P on outer circle. Join OP.
- Bisect OP, let M’ be the mid-point of OP. Taking M’ as centre and OM’ as radius draw a circle dotted which cuts the inner circle at M and P’.
- Join PM and PP’. Thus, PM and PP’ are the required tangents.
- On measuring PM and PP’, we find that PM = PP’ = 4 cm.
Actual calculation:
In right angle ∆OMP,
∠PMO = 90°
PM2 = OP2 – OM2 ...[By Pythagoras theorem i.e. (hypotenuse)2 = (base)2 + (perpendicular)2]
⇒ PM2 = (5)2 – (3)2
= 25 – 9
= 16
⇒ PM = 4 cm
Hence, the length of both tangents is 4 cm.
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