Circle
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Two chords, AB and CD, are drawn in a circle with center O. The chords are at the same perpendicular distance from the center, with OP = OQ. Using properties of circles and Pythagoras' theorem, it is shown that OA = OC and AP = CQ. Since the perpendicular from the center bisects each chord, 1/2AB = 1/2CD, and therefore AB = CD. The conclusion is that two chords at the same perpendicular distance from the center are equal in length.
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This document defines key terms related to circles such as radius, diameter, and chords. It states that the length of all chords at equal distances from the center of a circle are equal. This is proven using properties of right triangles and perpendicular bisectors - by showing two chords form two congruent right triangles with the radius, their lengths must be equal.
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circles-131126094958-phpapp01.pdf
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As one of my requirements for my demonstration. I am sharing this slide to also help you in your future needs.
Thank you and God bless.
CH 10 CIRCLE PPT NCERT
1. The document defines key terms related to circles such as radius, diameter, center, chord, arc, and sector.
2. It presents 8 theorems about properties of circles and relationships between chords, arcs, angles, and points on a circle. The theorems prove properties such as equal chords subtend equal angles at the center, angles subtended by an arc are double the angle at any other point on the circle, and if a line segment subtends equal angles at two points, all four points lie on a circle.
3. Diagrams and formal proofs using triangle congruence or properties of angles are provided for each theorem.
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This Dissertation explores the particular circumstances of Mirzapur, a region located in the
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9
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Circle
- 2. • O = CENTRE OF CIRCLE • AB = DIAMETER OF CIRCLE • CD = CHORD OF THE CIRCLE O CHORDS A B • C D
- 3. EQUAL CHORDS •DIAMETER IS THE LARGEST CHORD IN A CIRCLE. •AS THE CHORDS MOVE AWAY FROM THE CENTRE, THEIR LENGTHS DECREASE.
- 4. A
- 5. Two chords at the same perpendicular distance from the centre. Prove that they are of same length. •O
- 6. •O P A B C Let O be the centre and AB, CD be the chords at the same perpendicular distance OP and OQ from the centre. We want to show that AB = CD Join AO and CO. Consider OA = OC ( radii of the same circle ) OP = OQ ( given ) By Pythagoras theorem third sides are also equal, ie , AP = CQ ½ AB = ½ CD ( perpendicular from the centre bisects the chord) Therefore, AB = CD APO and CQO
- 7. “ TWO CHORDS AT THE SAME PERPENDICULAR DISTANCE FROM THE CENTRE ARE EQUAL LENGTH.”