Sum of Angles in Terms of tan⁻¹ – Part1 Theorem:  , Proof: Let  and , Where , , , , , From graph , , Where , = , , ⇒ x<0, y<0, , , , ⇒ x<(1/y), ⇒xy<1. Share Tweet View Email Print Follow

Properties of Triangle m – n Theorem m – n Theorem: Let D be a point on the side BC of Triangle ABC such that BD. DC = m: n and angle BAD = α, angle ADC = θ and angle DAC = β then (m + n) cot θ = n cot B – Read more about Properties of Triangle m – n Theorem[…]

Properties of Triangle – Theorem m – n Theorem: Let D be a point on the side BC of Triangle ABC such that BD. DC = m: n and angle BAD = α, angle ADC = θ and angle DAC = β then (m + n) cot θ = m cotα – n cotβ Proof: Read more about Properties of Triangle – Theorem[…]

Distance of The Orthocenter from Vertices and Sides of a Triangle Distance of The Orthocenter from Vertices and Sides of a Triangle: , , (  Projection of AC on AB) In triangle AFH, , , ,  = , Similarly, BH = 2RcosB and CH = 2R cosC  =FH/AF = FH/b cosA cotB = FH/ b Read more about Distance of The Orthocenter from Vertices and Sides of a Triangle[…]

Different Circles and Centers Connected with Triangle – Orthocenter Orthocenter(H) is the point of intersection of the altitudes of a triangle. Orthocenter (H) of an acute angled triangle lies inside the triangle. Orthocenter (H) of an obtuse angled triangle lies inside the triangle. Orthocenter(H) of a right-angled triangle ABC lies at the right angle itself. Read more about Different Circles and Centers Connected with Triangle – Orthocenter[…]

Incircle and Incenter – Length of Angle Bisector AP Length of Angle Bisector AP: Area of Triangle ABP + Area of Triangle ACP = Area of Triangle ABC ,                    ,       Similarly, length of angle bisector through point B and C is ,                                                                                                                          , Example: In Triangle ABC, the three bisectors of the angles Read more about Incircle and Incenter – Length of Angle Bisector AP[…]

Incircle and Incenter Distance of the Incenter from the Vertex: In triangle ABC ,    ,                                                            , , Similarly, , Length of Tangent from Vertices to the Incircle: In triangle , = s – b BD = BF = s – b Similarly, AF = AE = s – a And CD = CE = Read more about Incircle and Incenter[…]

Different Circles and Centers Connected with Triangle – Part2 Incircle and Incenter: The point of intersection of the internal bisectors of a triangle is called the incenter of the triangle. Also, it is the center of the circle touching all the three sides internally. Incenter always lies inside the triangle. Point AFIE, BDIF, and CEID Read more about Different Circles and Centers Connected with Triangle – Part2[…]

Different Circles and Centers Connected with Triangle – Part1 Circumcircle and Circumcenter: The circle passing through the angular point of Triangle ABC is called its circumcenter. The center of this circle is the point of intersection of the perpendicular bisectors of the sides and is called the circumcenter. its radius is denoted by R. Circumcenter Read more about Different Circles and Centers Connected with Triangle – Part1[…]

General Solution of Equation cos²θ = cos²α General Solution of Equation cos²θ = cos²α (or) sin²θ = sin²α: cos²θ = cos²α (since cos²θ + sin²θ = 1 ⇒ cos²θ = 1 – sin²θ)  (1 – sin²θ) = (1 – sin²α) (1 – sin²θ) – (1 – sin²α) = 0 sin²θ = sin²α sin²θ – sin²α Read more about General Solution of Equation cos²θ = cos²α[…]