Advertisement Remove all ads

The Area of Circle, Inscribed in Equilateral Triangle is 154 Cms2. Find the Perimeter of Triangle. - Mathematics

The area of circle, inscribed in equilateral triangle is 154 cms2. Find the perimeter of

Advertisement Remove all ads


Let circle inscribed in equilateral triangle

Be with centre O and radius ‘r’

Area of circle = 𝜋r2

ut given that area = 154 cm2.

𝜋r2 = 154

`22/7xxr^2 = 154`

𝑟2 = 7 × 7

r = 7cms

Radius of circle = 7cms

From fig. at point M, BC side is tangent at point M, BM ⊥ OM. In equilateral triangle, the perpendicular from vertex divides the side into two halves

BM = `1/2 BC = 1/2 (side =x) = x/2`

ΔBMO is right triangle, by Pythagoras theorem

`OB^2= BM^2+MO^2`

`OB=sqrt(r^2+(x^2/4 ))=sqrt(49+x^2/4)`OD=r

Altitude BD`=sqrt(3)/2(side)=sqrt(3)/2x=OB+OD`

BD – OD = OB






Perimeter =`3x=3xx14sqrt(3)`





  Is there an error in this question or solution?
Advertisement Remove all ads


RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Exercise 13.1 | Q 12 | Page 12
Advertisement Remove all ads
Advertisement Remove all ads

View all notifications

      Forgot password?
View in app×