Home
Class 9
MATHS
An equilateral triangle of side 9 cm is ...

An equilateral triangle of side `9 cm` is inscribed in a circle. Find the radius of the circle.

A

`3 cm `

B

`3 sqrt(2) cm`

C

`3 sqrt(3) cm`

D

`6 cm`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `Delta ABC ` be an equilateral triangle of side `9 cmgt`
Let `AD` be one of its medians.
Then , `AD _|_BC` and `BD = 4.5 cm`
`:. AD = sqrt( AB^(2) -BD^(2))= sqrt((9)^(2) - ((9)/(2))^(2))= sqrt((243)/(4))= (9sqrt(3))/( 2) cm`
Let `G` be the centroid of `Delta ABC`.
The, `AG : GD = 2:1`
`:. ` radius `= AG = (2)/(3) AD = ((2)/(3) xx (9 sqrt(3))/(2)) cm = 3 sqrt(3) cm`
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    RS AGGARWAL|Exercise MULTIPLE CHOICE QUESTION(MCQ)|37 Videos

  • CIRCLES

    RS AGGARWAL|Exercise EXERCISE 12C|26 Videos

  • BAR GRAPH, HISTOGRAM AND FREQUENCY POLYGON

    RS AGGARWAL|Exercise EXERCISE 17B|16 Videos

  • CONGRUENCE OF TRIANGLES AND INEQUALITIES IN A TRIANGLE

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|20 Videos

Similar Questions

Explore conceptually related problems

An equilateral triangle of side 9cm is inscribed in a circle.Find the radius of the circle.

An equilateral triangle of side 9cm is inscribed in a circle.Find the radius of the circle.

An equilateral triangle of side 6 cm is inscribed in a circle. Then radius of the circle is

A circle is inscribed in a square. An equilateral triangle of side 4sqrt(3) cm is inscribed in that circle. The length of the diagonal of the square (in centimetres) is

An equilateral triangle is inscribed in a circle of radius 6cm. Find its side.

A circle is inscribed in an equilateral triangle and square is inscribed in that circle. The ratio of the areas of the triangle and the square is

If a square of side x and an equilateral triangle of side y are inscribed in a circle, then what is the ratio of x to y ?

In the given figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region. [Use sqrt(3)=1.73 and pi=3.14 ]

In an equilateral triangle of side 24cm, a circle is inscribed touching its sides.Find the area of the remaining portion of the triangle ( Take sqrt(3)=1.732)

An equilateral triangle ABC is inscribed in a circle of radius r if P be any point on the circle then find the value of PA^(2)+PB^(2)+PC^(2)