Advertisements
Advertisements
प्रश्न
The area of the largest triangle that can be inscribed in a semi-circle of radius r, is
पर्याय
r2
2r2
r3
2r3
उत्तर
The triangle with the largest area will be symmetrical as shown in the figure.
Let the radius of the circle be r.
Hence,
`ar (Δ ABC)=1/2(r)(2r)`
`= r^2` sq.unit
APPEARS IN
संबंधित प्रश्न
A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take π = 3.14)
In the given figure ABCD is quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD and CM ⊥ BD such that AL = 9cm and CM = 12 cm. Calculate the area of the quadrilateral.
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc. (Use π = `22/7`)
A rectangular park is 100 m by 50 m. It is surrounding by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre (use π = 3.14).
A circle is inscribed in an equilateral triangle ABC is side 12 cm, touching its sides (the following figure). Find the radius of the inscribed circle and the area of the shaded part.
ABCDEF is a regular hexagon with centre O (in the following figure). If the area of triangle OAB is 9 cm2, find the area of : (i) the hexagon and (ii) the circle in which the haxagon is incribed.
In the following figure, AB = 36 cm and M is mid-point of AB. Semi-circles are drawn on AB, AM and MB as diameters. A circle with centre C touches all the three circles. Find the area of the shaded region.
The length of an arc of a circle, subtending an angle of 54° at the centre, is 16.5 cm. Calculate the radius, circumference and area of the circle.
The radius of a wheel is 0.25 m. How many revolutions will it make in covering 11 km?
Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centers is 14 cm. Find the radii of the circles.
