Home
Class 11
MATHS
There is a point P inside an equilateral...

There is a point `P` inside an equilateral ` A B C` of side `a` whose distances from vertices `A , Ba n dCa r e3,4a n d5,` respectively. Rotate the triangle and `P` through `60^0` about `Cdot` Let `A` go to `A^(prime)a n dPtoP^(prime)dot` Then the area of `P A P^(prime)` (in sq. units) is 8 (b) 12 (c) 16 (d) 6

Promotional Banner

Similar Questions

Explore conceptually related problems

In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then find the area of A B Cdot

In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then find the area of A B Cdot

Let f(1)=-2a n df^(prime)(x)geq4. 2for1lt=xlt=6. The smallest possible value of f(6) is 9 (b) 12 (c) 15 (d) 19

A B C is an equilateral triangle of side 4c mdot If R ,ra n dh are the circumradius, inradius, and altitude, respectively, then (R+h)/h is equal to 4 (b) 2 (c) 1 (d) 3

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Consider a triangle A B C and let a , ba n dc denote the lengths of the sides opposite to vertices A , B ,a n dC , respectively. Suppose a=6,b=10 , and the area of triangle is 15sqrt(3)dot If /_A C B is obtuse and if r denotes the radius of the incircle of the triangle, then the value of r^2 is

The probability that at least one of Aa n dB occurs is 0.6. If Aa n dB occur simultaneously with probability 0.3, then find the value of P(A^(prime))+P(B^(prime))dot

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is (a)4:1 (b) 2:1 (c) 8:3 (d) 7:3

The radii r_1, r_2,r_3 of the escribed circles of the triangle A B C are in H.P. If the area of the triangle is 24 c m^2a n d its perimeter is 24cm, then the length of its largest side is 10 (b) 9 (c) 8 (d) none of these

Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA C are extended up to Ea n dF , respectively, such that B ExC F=A B^2dot Prove that the line E F always passes through a fixed point.