The radius of the circle inscribed in an equilateral triangle with side 6 cm is m√3 cm. Then m=
Answers
Step-by-step explanation:
I HOPE IT WILL HELP U
PLEASE MARK ME AS BRAINLIEST ANSWER
Answer:
Radius of circle = OC = 2√3 cm and value of m = 2.
Step-by-step explanation:
Equilateral triangle:
- An equilateral triangle is one in which all of its sides are equal and have an equal angle.
- The equilateral triangle also has the same interior angles, which are 60 degrees.
Let ABC be an equilateral triangle with side 6cm inscribed in a circle of radius m√3 cm
AB = BC = CA = 6cm
Let O be the center of the circle then
OA = OB = OC = m√3cm
Let OD be the perpendicular from O on side BC, then D is the mid-point of BC.
then DC = BC/2
= 6/2
DC = 3
OB and OC are bisectors of ∠B and ∠C respectively.
So, ∠OCD = 30°.
In ΔOCD, is a right angled triangle with 90° at angle D.
we have ∠OCD = 30°, OC = m√3cm and DC = 3cm
By trigonometric ratios,
cos(OCD) = DC/OC [cosθ = adjacent side/hypotenuse]
cos30° = 3/OC
√3/2 = 3/OC
OC = (3×2)/√3
OC = (√3×√3×2)/√3
OC = 2√3 cm
Radius of circle = OC = 2√3 cm.
Hence, value of m = 2.
Know more about Equilateral triangle:
brainly.in/question/8670402
brainly.in/question/32849987
