Incentre

Q.

A man running on a race course notes that sum of its distances from two flags posts from him is always 10m and the distance between the flag posts is 8m. He notes that he can read the messages of value system 'HONESTY'and 'RESPECT FOR OTHER'on the poles which ever side he moves. Find the equation of the path traced by the man. Do you think these value systems are necessary in life?

Q.

Find the equation of the circle passing through the points (1, -2) and (4, -3) and whose centre lies on the line 3x + 4y = 7.

Q.

The coordinates of the points O, A and B are (0, 0), (0, 4) and (6, 0) respectively. If a points P moves such that the

area of $△$POA is always twice the area of $△$POB, then the equation to both parts of the locus of P is

1. 

2. 

3. 

4. None of these

Q. Using the section formula, prove that the three points
A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1) are collinear.

Q.

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid point of the base is at origin. Find the vertices of the triangle.

Q. Solve the inequality for real $x$.

Q. The x-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as (0, 1), (1, 1) and (1, 0) is

1. $2-\sqrt{2}$
2. $2+\sqrt{2}$
3. $1+\sqrt{2}$
4. $1-\sqrt{2}$

Q. Solve the equation : ${3x}^2-4x+\frac{20}{3}=0$

Q.

The coordinates of the feet of the perpendiculars from the vertices of a triangle on the opposite sides are $(20,25),(8,16)$ and $(8,9)$. The coordinates of a vertex of the triangle are

1. (5, 10)

2. (50, -5)

3. (15, 30)

4. (10, 15)