Circles Theorem | Equal chords subtends equal segments within the circle

http://www.learncbse.in/ncert-solutions-for-class-9-maths/

CBSE Class 9 mathts NCERT Solutions Chapter 10 Circles Ex 10.3 Q3

00:02 Circles Theorem:If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.

00:20 Construction to solve the Above Circle theorem

02:00 Apply S.S.S rule of Congruency

02:20 Apply CPCT (Corresponding Parts of Congruent Triangles)

03:23 Apply S.A.S rule of Congruency

03:36 Apply CPCT

04:10 Using Linear Pair

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In this video, students learn aplication of Circles theorems (Several Theorems) and sample problems relating circles and associated angles.

Circles theorem 1. A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane.

Circles theorem 2. Equal chords of a circle (or of congruent circles) subtend equal angles at the centre.

http://www.learncbse.in/ncert-solutions-for-class-9-maths/

Circles theorem 3. If the angles subtended by two chords of a circle (or of congruent circles) at the centre(corresponding centres) are equal, the chords are equal.

Circles theorem 4. The perpendicular from the centre of a circle to a chord bisects the chord.

Circles theorem 7. Equal chords of a circle (or of congruent circles) are equidistant from the centre (or corresponding centres).

Circles theorem8. Chords equidistant from the centre (or corresponding centres) of a circle (or of congruent circles) are equal.

Circles theorem 9. If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs (minor, major) are congruent.

Circles theorem 10. Congruent arcs of a circle subtend equal angles at the centre.

Circles theorem 11. The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Circles theorem 12. Angles in the same segment of a circle are equal.

Circles theorem 13. Angle in a semicircle is a right angle.

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Reference book for the above video is

National Council of Educational Research and Training (NCERT) Book for Class 9 Subject: Maths

This Video is also refers as CBSE Class 9 mathts NCERT Solutions Chapter 10 Circles Ex 10.4

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