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Jay county drug bustBrahmagupta dedicated a substantial portion of his work to geometry and trigonometry. He established √10 (3.162277) as a good practical approximation for π (3.141593), and gave a formula, now known as Brahmagupta’s Formula, for the area of a cyclic quadrilateral, as well as a celebrated theorem on the diagonals of a cyclic quadrilateral ... GEOMETRY OF CIRCLES: CYCLIC QUADRILATERALS & TANGENTS 4 AUGUST 2014 Lesson Description In this lesson we: Apply the theorems about cyclic quadrilaterals and tangents to a circle to solving riders Challenge Question Two concentric circles, centred at O, have radii of 5 cm and 8,5 cm respectively. QR = 6 cm and OT PS.

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Figure 7: Cyclic Quadrilateral 2.1 Angles If 2 is a cyclic quadrilateral, then O 2 ¡ ` O 4¢ £ ¤ ¥ ¦ Conversely, if _ 2 ¡ 4¢ £ ¤ ¥ or if B 2 1 O 4¢, then 2 is a cyclic quadrilateral. 2.2 Ptolemy’s Theorem For a cyclic quadrilateral as in Figure 7, we have: 4§ 2 ¨ J O§ O ` O§ .¦ mention Brahmagupta’s results on the cyclic quadrilateral, see e.g. [Cajori, 1991]. The formula was extended to non-cyclic quadrilaterals, and to polygons with ﬁve sides or more, but these developments belong to modern mathematics. Their methods do not shed light on the problem at hand, and are therefore not discussed here. Example showing supplementary opposite angles in inscribed quadrilateral. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

1 4 In the diagram, O is the centre of the circle. Angle OAC - 120 and angle BOC - 80 Calculate the size of the followmg angles, giving a geometrical reason for each of your answers.