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1.
In 
, if 
, then 
is equal to
, if , then is equal to
2.
Three vertical poles of heights 
and 
at the vertices 
and 
of a 
subtend angles 
respectively at the circumcentre of the triangle. If 
and 
are in AP, then 
are in
and at the vertices and of a subtend angles respectively at the circumcentre of the triangle. If and are in AP, then are in
3.
The area enclosed within the curve 
is
is
4.
is a point on the segment joining the feet of two vertical poles of height 
and 
The angles of elevation of the top of the poles from are 45
each. Then, the square of the distance between the top of the poles is
is a point on the segment joining the feet of two vertical poles of height and The angles of elevation of the top of the poles from are 45 each. Then, the square of the distance between the top of the poles is
5.
By rotating the coordinates axes through 
in anticlockwise sense the equation 
changes to
in anticlockwise sense the equation changes to
6.
The 
-coordinate of the incentre of the triangle where the mid points of the sides are (0, 1), (1, 1)and (1, 0) is
-coordinate of the incentre of the triangle where the mid points of the sides are (0, 1), (1, 1)and (1, 0) is
7.
Let 
and 
be vertices of a triangle
. If the centroid of this triangle moves on the line 
, then the locus of the vertex is the line
and be vertices of a triangle. If the centroid of this triangle moves on the line , then the locus of the vertex is the line
8.
The angle of elevation of the top of a tower at a point on the ground is . If on walking 20 m toward the tower the angle of elevation becomes 
, then the height of the tower is
. If on walking 20 m toward the tower the angle of elevation becomes , then the height of the tower is
9.
In a , if 
and 
, then the value of is
, if and , then the value of is
10.
If 
denote the length of the perpendiculars from the origin on the lines 
and 
respectively, then 
is equal to
denote the length of the perpendiculars from the origin on the lines and respectively, then is equal to