Ch 9 covers circle geometry: properties of chords, arcs, angles subtended by chords and arcs, and cyclic quadrilaterals. Students prove important circle theorems.
The perpendicular from the centre to a chord bisects the chord. Equal chords are equidistant from the centre (and conversely). Equal chords subtend equal angles at the centre.
The angle subtended by an arc at the centre is twice the angle subtended at any point on the remaining part of the circle. Angles in the same segment are equal. An angle in a semicircle is always 90°.
A cyclic quadrilateral has all four vertices on a circle. The sum of opposite angles of a cyclic quadrilateral is 180°. Conversely, if opposite angles of a quadrilateral sum to 180°, it is cyclic.
Download: https://ncert.nic.in/textbook/pdf/iemh109.pdf | Complete book: https://ncert.nic.in/textbook/pdf/iemh1ps.zip
A cyclic quadrilateral is a four-sided figure whose all four vertices lie on a single circle (circumscribed circle). Its key property: opposite angles sum to 180°.
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