O Level Math - Don't Go Around In Circles Solving A Circles Question

Don’t get thrown off by seemingly complicated diagrams.

You start by first observing for ALL the shapes and structures that relate to the properties of a circle - they are there for a reason: to guide you. 

It is very likely that the question setter's suggested solution to the question makes use of ALL the hints available (of course there may be more elegant solutions that exist). Hence, note down ALL the hints, then start to manipulate the equations and you'll arrive at your answer. 

Observation	Relevant Properties
Radius & Tangent	Radius perpendicular to tangent
Butterfly	Angles in same segment
Angle at centre	Angle at centre = Twice angle at circumference
Diameter	Angles in semicircle
Chords from contact with tangent	Angle in alternate segment
Chords	Bisector of Chord & Perpendicular of Chord; Equal Chords & Chords equidistant from centre
Cyclic quadrilaterals	Opposite Angles of cyclic quad; External angle of cyclic quad
Tangents	Tangent perpendicular to radius; Tangents from external point: Equal Tangents & Angle between tangents equal; Angles between radii equal; Angles in alternate segment (Alternate Segment Theorem)

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