GEOMETRY key points
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12/18/2011
CBSE
 The tangent at any point of a circle is perpendicular to the radius
through the point of contract.  A circle is the set of all points in a plane which are at a constant
distance from a fixed point in the plane.  The line joining the centre of a circle to the mid point of a chord is
perpendicular to the chord.  There is one and only one circle passing through three non collinear
points.  If a side of a cyclic quadrilateral in produces, then the exterior angle
is equal to the interior opposite angle.  Suppose a circle of radius r is inscribed in a triangle of area A. If the
semi perimeter of the triangle be s then
 If all the sides of a parallelogram touch a circle, the parallel gram is a
rhombus.  The lengths of two tangents drawn from an external point to a circle are
equal.  Two figures having same shapes and same size are called congruent while
two figures having the same shape (and not necessarily the same size) are
called similar figures.  The line joining the mid points of any two sides of a triangle is parallel
to the third and equal to half of it.  According to Thales, if corresponding of two triangles are equal, then
they are known as equiangular triangles, and the ratio of any two
corresponding sides in two equiangular triangles is always the same.  If a line divides any two sides of a triangle in the same ratio, then the
line is parallel to the third side.  If two triangles are similar then in these triangles corresponding angles
are equal and their corresponding sides are also in the same ratio.  Circum centre is the point of intersection of the perpendicular bisectors
of the sides.  According to Pythagoras in a triangle, if square of one side is equal to
the sum of the square of the other two sides, then the angle opposite the
first side is a right angle.  If two angles of a triangle are unequal, the greater angle has the greater
side opposite to it.  If you want to draw a tangent at a point of a circle, simply draw the
radius through this point and this will be the required tangent at the point.  Two lines having a common point are known as intersecting lines. Two lines
can intersect at the most at one point.  Given two distinct points A and B, there is one and only one line that
contains both the points.  If a point lies on the circle, then there is only one tangent to the
circle at this point.  Inclination between two rays having a common end point is called an angle.
 If one side of triangle is produces, then the exterior angle so formed is
equal to the sum of two interior opposite angles.