Question

in the given figure, if radius is 3cm find the perimeter of triangle abc

Answer 1

Hi Sushant,

your answer is 36 cm

in triangle BOC
let D be mid point of BC
so in triangle ODC (right triangle since BC is tangent)
OC = hypotenuse = 3√5 cm
OD = radius = 3 cm (given)
so DC^2 = (3√5)^2-3^2 = 45 - 9 = 36 (pythagoras theorem)
DC = 6 cm

so BC = 2DC = 12 cm

now the triangle ABC is equilateral since
<BOC = 360/3 = 120
in triangle BOC
<OCB = <OBC (since OB = OC)
 <OCB+<OBC= 180-<BOC
= 180-120
= 60
hence <OCB = <OBC = 30

now
<ACO = <OCB since OC is angle bisector
so
<ACO = 30
now <ACO + <OCB = 60 = <C

similarly <B = 60
therefore <A = 60

hence its an equilateral triangle with side BC = 12cm
hence perimeter is 12+12+12 = 36 cm

Hope it helped.
Let me know if any doubts.
Cheers !!!