GEOMETRY FORMULAE

B.P.T.

AP = AQ PB QC

Apollonius' theorem

AB2 + AC2 = 2AD2 + 2BD2 SIMILARITY OF TRIANGLES.

∆ ABC ∼ ∆ PQR

AB = BC = AC [C.S.S.T] PQ QR PR

[Areas of Similar Triangles]

A(∆ ABC) AB = BC = AC A(∆ PQR) PQ QR PR

Right angled triangles,

AC2 = AB2 + BC2           [By Pythagoras theorem] BD2 = AD × DC          [Geometric mean] ∆ ABC ∼ ∆ ADB ∼ ∆ BDC [Similarity of right angled triangles]

In a 300 – 60 0 – 900 triangle.

Side opposite to 300 = ½ Hypotenuse

Side opposite to 600 = (√3/2)Hypotenuse

In a 450  - 450 – 900 triangle

Side opposite to 450 =(1/√2) Hypotenuse

Tangent – Secant Theorem

PA × PB = PT2