Q1.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.
Answers
Answer:
Explanation:
Given, two concentric circles of radius 4 cm and 6 cm with common centre O. We have to draw two tangents to the inner circle from a point of the outer circle.
Steps of Construction:
1. Draw two concentric circles with centre an O and radii 4 cm and 6 cm.
2. Take any point P on the outer circle. Join OP.
3. Now, bisect OP. Let M' be the mid-point of OP.
3. Taking M' as a centre and OM' as radius draw a circle (dotted) which cuts the inner circle at M and P'.
4. Join PM and PP'. Thus, PM and PP' are required tangents.
5. On measuting PM and PP', we get PM = PP' = 4.47 cm.
Calculation:
In right ΔOMP, ∠PMO=90∘
∴ PM2=OP2−OM2 (by Pythagoras theorem)
⇒ PM2=(6)2−(4)2=36−16=20
⇒ PM=20−−√=44.47
Hence, the length of the tangent is 4.47.
Justification: Join OM and OP' which are radius.
The ∠OMP is an angle that lies in the semi-circle and therefore, ∠OMP=90∘
⇒ OM⊥OP
Since,
Om is the radius of the circle, so MP has to be a tangent to the circle. Similarly, PP' is also a tangent to the circle.
