Hello, Aveek Agrawal!

1) Triangle is inscribed in a circle.

The bisector of meets side at and the circle at

Line segment QC is drawn.

If , findbisectsCode:B * * * * / \ * * / \ * * / \ * Q * / \ * * / \ * * * / * \ * * / θ * \ * * / * θ \ * A *- - - - - - - - -* C * * * * * * *

Draw chord

An inscribed angle is measure by one-half its intercepted arc.

Since , then

Since . . . then

Therefore: .

2) is a cyclic trapezium in which

Show that: .Since , then: /Code:A * * * D * - - - - - * */ \* */ \* / \ B * - - - - - - - - - * C * * * * * * * * * * * * *

. . Parallel chords intercept equal arcs.

Add to both sides:

. .

Since: .