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 :┬а┬а┬а┬а┬а┬а┬а
(i)┬аDraw two concentric circleswith centre O and radii 3 cm and 5 cm.
(ii)┬аTaking any point P onouter circle. Join OP.
(iii)┬аBisect OP, let MтАЩ be themid-point of OP.
Taking MтАЩ as centre and OMтАЩ as radius draw a circle dotted which cuts the innercircle as M and PтАЩ.
(iv)┬аJoin PM and PPтАЩ. Thus, PMand PPтАЩ are the required tangents.
(v)┬аOn measuring PM and PPтАЩ, wefind that PM = PPтАЩ = 4 cm.
Actual calculation:
In right angle ╬ФOMP, тИаPMO =90┬░
тИ┤ PM2┬а=OP2┬атАУ OM2
[by Pythagoras theorem i.e. (hypotenuse)2┬а= (base)2┬а+(perpendicular)2]
тЗТ PM2┬а=(5)2┬атАУ (3)2┬а= 25 тАУ 9 = 16
тЗТ PM = 4cm
Hence, the length of both tangents is 4 cm.