Complex Numbers with Vector Addition is obtained using the sides of triangles, the sum of sides of two sides of a triangle is greater than the other side. Worked Examples of Complex Numbers with Vector Addition Suppose \( \displaystyle 0 \lt \alpha, \ \beta \lt \frac{\pi}{2} \) and define complex numbers \(z_n\) by $$z_n = […]

# Tag Archives: Cyclic Quadrilateral

# Collinear Proof in Circle Geometry

(a) \( \ \ \) Show that \( \angle DSR = \angle DAR \). The quadrilateral \( DRAS \) is cyclic, since \( \angle DRA + \angle DSA = \pi (180^{\circ}) \). Therefore \( \angle DSR = \angle DAR \) (angles in the same segment of circle \( DRAS \), both standing on same chord […]

# Cyclic Quadrilateral in Circle Geometry

A cyclic quadrilateral is inscribed into a circle, whose vertices all lie on a circle. The properties of cyclic quadrilateral in circle geometry are; Opposite angles in a cyclic quadrilateral supplementary. Exterior angle and its opposite angle are equal. (a) Prove that \( FADG \) is a cyclic quadrilateral. \( \begin{aligned} \require{color}\text{Let } \angle BCD […]