# Important Formulae of Mathematics (Geometry, Trigonometry, Co-ordinate Geometry – For SSC, IBPS, etc.)

Check out important Formulae of Mathematics related to Geometry, Trigonometry, and Co-ordinate Geometry. These are important for SSC, RBI, IBPS exams, etc.

**GEOMETRY**

1) A triangle with sides a,b and c and radius of incircle and circumcircle as r and R respectively then the relation between them is as follows

r = area of triangle/ semiperimeter

R = abc/4*area of triangle = abc/4*r*semiperimeter

2) And in case of right angled triangle with perpendicular as a base as b and hypotenuse as h, then

R = hypotenuse/2

r = (perpendicular + base – hypotenuse)/2

3) Area of triangle when one angle and two sides are given = 1/2(ab sinC)=1/2(ac sinB)=1/2(bc sin A)

4) If AD is the bisector of angle BAC of triangle ABC then

AB/AC=BD/DC

5) And if AD is median, then

**AB ^{2}+AC^{2}=2(AD^{2}+BD^{2} or DC^{2}**

6) The ratio of area of two similar triangles is equal to the square of the corresponding medians or altitudes or sides or angle bisector segments.

7) In right angled triangle ABC, angle B= **90 ^{0}** and BD perpendicular AC, then

**BD ^{2} = AD*DC**

8) The area of equilateral triangle described on the side of the square is half the area of eq. triangle described on its diagonals.

9) In triangle ABC, angle B is obtuse and AD is perpendicular to CB produced, then

**AC ^{2} = AB^{2}+BC^{2}+2BC*BD **

And, in the case of B being acute angle and AD is perpendicular to BC, then

**AC ^{2} = AB^{2}+BC^{2}-2BC*BD**

ABC is right angled triangle, angle B=90 degree, and D and E are points on AB and AC, then

**AE ^{2}+CD^{2}=AC^{2}+DE^{2}**

And if D and E are midpoints, then

**4AE ^{2}=4AC^{2}+BC^{2}**

**4CD ^{2}=4BC^{2}+AC^{2}**

**4(AE ^{2}+CD^{2})=5AC^{2}=20DE^{2}**

10) Angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

11) Angle in the same segment are equal.

12) When two chords AB and AC of circle cuts each other inside or outside the circle, then

AP*BP=CP*DP

13) When chord AB of a circle is produced to a point P, and from that point a tangent is drawn to the circle, then

**PT ^{2}=PA*PB**

14) When a chord XY is drawn parallel to tangent APB, then angle APX=angle PYX, angle BPY=angle PXY

15) Two circles with radius r and R, and the distance between them is d, then

Measure of direct tangent = Square root [** d ^{2} – (R-r)^{2 ]}**

Measure of transverse tangent = Square root[**d ^{2} + (R+r)^{2}**]

Where, R&r

When two circles with equal radius r intersect each other at its center, the length of common chord = r* Square root( 3)

**TRIGONOMETRY**

**1) If sin A + cos A = x, then, sin A – cos A = Square root ( 2 – x ^{2)}**

**2) If sec A + tan A = x, then, sec A = (x ^{2} + 1)/2x**

**3) Maximum value of (sin A*cos A) ^{n} =( 1/2)^{n} , therefore sin A*cos A = ½**

**4) In the angle of incidence made by a point on the land to the top of a pole is A and after travelling the distance D the angle of incidence become B then, height of the pole **

**H = D/(cot A – cot B), where A>B**

**5) If the angle of depression from top and bottom of a pole with the second pole is A and B respectively, and the height of the second pole is H, then**

**Height of the first pole = H sin(A+B)/cos A*cos B**

**6) If the angle of depression of top and bottom of tree from the top of the pole is A and B respectively, and height of the tree is h, then the height of the pole, H = h tan A/tan A*tan B**

7) If Sec x + Tan x= 2, then Sec x – tan x= 1/2

8) Tanx. tan 2x. tan 4x= tan 3x

9) sinx. sin 2x. sin 3x= 1/4* sin 3x

10) cos x. cos 2x. cos 3x = 1/4* cos 3x

**CO-ORDINATE GEOMETRY**

**1) The distance measured from origin O along X- axis is called abscissa and along Y- axis is called ordinate.**

**2) Abscissa along Y-axis is 0 and ordinate along X-axis is 0.**

**3) The slope or gradient of a line is denoted by m and its intercept is denoted by c**

**For equation ax+by+c=0, then m = -a/b , and c = -c/b**

**4) If the vertices of triangle is denoted by (x _{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3}), then its area is**

**½[x _{1}(y_{2}-y_{1})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}) and its incentre = [ax_{1}+bx_{2}+cx_{3}]/a+b+c , [ay_{1}+by_{2}+cy_{3}]/a+b+c , and centroid = [x_{1}+x_{2}+x_{3}/3] , [y_{1}+y_{2}+y_{3}/3]**

**5) If (x _{1},y_{1}) and (x_{2},y_{2}) is coordinate of two points on the line then **

**m= y _{2}-y_{1}/x_{2}-x_{1}**

We will update this post with more important formulae of Trigonometry, Geometry and Co-ordinate Geometry in the next few days. You are, thus, advised to bookmark this page and visit here again.