Question -
Answer -
Given, two concentric circles of radii 3 cm and 5 cm with centreO. We have to draw pair of tangents from point P on outer circle to the other.
Steps of construction :
(i) Draw two concentric circleswith centre O and radii 3 cm and 5 cm.
(ii) Taking any point P onouter circle. Join OP.
(iii) Bisect OP, let M’ be themid-point of OP.
Taking M’ as centre and OM’ as radius draw a circle dotted which cuts the innercircle as M and P’.
(iv) Join PM and PP’. Thus, PMand PP’ are the required tangents.
(v) On measuring PM and PP’, wefind that PM = PP’ = 4 cm.
Actual calculation:
In right angle ΔOMP, ∠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 = 4cm
Hence, the length of both tangents is 4 cm.