Video lectures of KAMAL SIR for Properties of triangles
In a triangle ABC the angles are denoted by capital letters A, B and C and the length of the sides opposite to these angles are denoted by small letters a, b and c. Semi perimeter of the triangle is
given by s where 2s = a + b+c and its area is denoted by Δ
Sine rule is an important tool that relates side lengths with angles of triangles and circum radius of triangle
NAPIER’S ANALOGY (TANGENT RULE)
In a triangle ABC
(i) a = b cos C + c cos B (ii) b = c cos A + a cos C (iii) c = a cos B + b cos C
HALF ANGLE FORMULAE
CENTROID AND MEDIANS OF A TRIANGLE
The line joining any vertex of a triangle to the mid point of the opposite side of the triangle is called the median of the triangle. The three medians of a triangle are concurrent and the point of concurrency of the medians of any triangle is called the centroid of the triangle. The centroid divides the median
in the ratio 2 : 1.
The circle which passes through the angular points of a ABC, is called its circumcircle. The centre of this circle i.e., the point of concurrency of the perpendicular bisectors of the sides of the ABC, is called the circumcenter.
Radius of the circumcircle is given by the following formulae
BISECTORS OF THE ANGLES
If AD bisects the angle A and divide the base into portions x and y, we have, by Geometry,
the circle which can be inscribed within the triangle so as to touch each of the sides of the triangle is called its incircle. The centre of this circle i.e., the point of concurrency of angle bisectors of the triangle is called the incentre of the ABC
The distances Between the special points
The circle which touches the side BC and the two sides AB and AC produced is called the escribed circle opposite the angle A. Its centre and radius will be denoted by I1 and r1 respectively.
The triangle formed by joining the three excentres I1, I2 and I3 of
DABC is called the excentral or excentric triangle. Not that
Inscribed & Circumscribed Polygons
SOLUTION OF TRIANGLES
When any three of the six elements (except all the three angles) of a triangle are given, the triangle is known completely. This process is called the solution of triangles.