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It states that the internal bisector of an angle of a triangle divides the opposite side in the ratio of adjacent sides.
DCT (Direct Common Tangent) and TCT (Transverse Common Tangent) are used for length of tangents between two non-intersecting circles.
Volume = (1/3)πh (R² + r² + Rr), where h is height, R and r are radii.
a/sinA = b/sinB = c/sinC = 2R, where R is the circumradius of the triangle.
Hollow cylinder volume = πh(R² - r²); solid cylinder volume = πR²h.
It solves ratio problems in triangles and cevians using weighted averages without coordinate geometry.
The orthocenter lies at the vertex of the right angle in a right-angled triangle.
sin(90°-θ)=cosθ, cos(90°-θ)=sinθ, tan(90°-θ)=cotθ.
Non-parallel sides are equal, base angles are equal, and diagonals are equal.
Circumcenter is the intersection of perpendicular bisectors, lying inside an acute triangle.
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It states that the internal bisector of an angle of a triangle divides the opposite side in the ratio of adjacent sides.
DCT (Direct Common Tangent) and TCT (Transverse Common Tangent) are used for length of tangents between two non-intersecting circles.
Volume = (1/3)πh (R² + r² + Rr), where h is height, R and r are radii.
a/sinA = b/sinB = c/sinC = 2R, where R is the circumradius of the triangle.
Hollow cylinder volume = πh(R² - r²); solid cylinder volume = πR²h.
It solves ratio problems in triangles and cevians using weighted averages without coordinate geometry.
The orthocenter lies at the vertex of the right angle in a right-angled triangle.
sin(90°-θ)=cosθ, cos(90°-θ)=sinθ, tan(90°-θ)=cotθ.
Non-parallel sides are equal, base angles are equal, and diagonals are equal.
Circumcenter is the intersection of perpendicular bisectors, lying inside an acute triangle.
