Question

The area of the largest triangle with base 8cm which can be formed inside a circle of radius 5cm is ___ .

Answer 1

Consider a triangle ABC

Consider BC to be the base 8cm, So the base will be a sector of the circle it is inscribed in.

So point A will be the point were the line perpendicular to the base BC intersects the circumference of the circle.

So the height of the triangle will be the sum of the radius and the perpendicular distance between the centre of the circle and base.

i.e,

$AD=AO+OD$

AO=radius=5cm;

$OD=\sqrt{O{B}^2-B{D}^2}$

OD= 3cm

AD=8cm

So area of triangle is;

$=\frac{1}{2}$*AD*BC

=32