The triangle of maximum area that can be inscribed in a given circle of radius ′r′ is:
A
A right-angle triangle having two of its sides of length 2r and r
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
An equilateral triangle of height 2r3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Isosceles triangle with base equal to 2r
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
An equilateral triangle having each of its side of length √3r
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is D An equilateral triangle having each of its side of length √3r Triangle of maximum area that can be inscribed in a circle is an equilateral triangle. Let △ABC be inscribed in circle, Now, in △OBD OD=rcos60∘=r2
Height =AD=3r2
Again in △ABD
Now sin 60∘=3r/2AB ⇒AB=√3r