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CBSE Class 9 Answered

If two intersecting chors of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.
Asked by sujaysarkar84 | 09 Mar, 2015, 05:35: PM
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C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
C o n s i d e r space a space c i r c l e space w i t h space c e n t r e space a t space O. L e t space A B space a n d space C D space b e space t h e space i n t e r s e c t i n g space c h o r d s space w h i c h space m a k e space e q u a l space a n g l e s space w i t h space t h e space d i a m e t e r space P R space p a s sin g t h r o u g h space Q. W e space n e e d space t o space p r o v e space t h a t space A B equals C D L e t space M space a n d space N space a r e space t h e space f o o t space o f space p e r p e n d i c u l a r s space f r o m space t h e space c e n t r e space t o space t h e space c h o r d s. N o w space c o n s i d e r space triangle O Q M space a n d space triangle O Q N angle O M Q equals angle O N Q equals 90 degree angle O Q M equals angle O Q N space space space space space open square brackets G i v e n close square brackets O Q equals O Q space space space space space space space space space space space space space space space space space open square brackets c o m m o n close square brackets T h u s comma space b y space A n g l e minus A n g l e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e comma space triangle O Q M approximately equal to triangle O Q N T h e space c o r r e s p o n d i n g space p a r t s space o f space t h e space c o n g r u e n t space t r i a n g l e s space a r e space c o n g r u e n t. T h u s comma space O M equals O N. W e space k n o w space t h a t space e q u i d i s tan t space c h o r d s space f r o m space t h e space c e n t r e space o f space t h e space c i r c l e space a r e space e q u a l space i n space l e n g t h T h u s comma space w e space h a v e comma A B equals C D
Answered by Vimala Ramamurthy | 11 Mar, 2015, 09:21: AM

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CBSE 9 - Maths
prove that of all chords of circle through a given point within it, the chord which is bisected at that point is the smallest
Asked by subbusuchi1978 | 05 Nov, 2023, 10:24: AM
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CBSE 9 - Maths
if two circles intersect at two points prove that their centres lie in the perpendicular bisector of the common chord
Asked by rameshsonkar1234ramesh | 21 Dec, 2022, 11:03: PM
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CBSE 9 - Maths
three girls Reshma Salma And Mandeep are playing a game by standing on a circle of radius 5 drawn in a park Reshma throws a ball to Salma Salma To mandip mandip to Reshma if the distance between Reshma and Salman and between Salman Mandeep 6 each what is the distance between Reshma Mandip
Asked by chalkekalyani80 | 06 Mar, 2022, 11:25: AM
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CBSE 9 - Maths
two circles of radii 5cm and 3cm intersect at two points and distance between the centres is 4cm. find the length of the common chord  
Asked by tejvinder3r | 27 Jan, 2020, 10:27: AM
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CBSE 9 - Maths
AC is the diameter of the circle whose centre is O .AB and CD are parallel chords of a circle .prove that OA = OB 
Asked by arvindhsb2005 | 14 Jan, 2020, 09:14: PM
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CBSE 9 - Maths
Q. Out of two concentric circles,the radius of the outer circle is 5 cm and the chord AC of length 8 cm is tangent to the inner circle.Find the radius of the inner circle.
Asked by sambitgenius2005 | 24 Apr, 2019, 08:03: PM
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CBSE 9 - Maths
Prove that the line joining the mid points of two parallel chords of a circle, passes through the centre of the circle.
Asked by Topperlearning User | 18 Aug, 2017, 09:07: AM
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CBSE 9 - Maths
Prove that the perpendicular from the centre of the circle to a chord bisects the chord.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 9 - Maths
AB and CD are two parallel chords of a circle such that AB = 12 cm and CD = 24 cm. The chords are on the opposite sides of the centre and the distance between them is 17 cm. Find the distance between them.
Asked by Topperlearning User | 14 Feb, 2014, 02:05: PM
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CBSE 9 - Maths
begin mathsize 12px style Two space chords space AB space and space AC space of space straight a space circle space are space equal. space Prove space that space the space centre space of space the space circle space lies space on space the space angl e space bisector space of space angle BAC. end style
Asked by Topperlearning User | 29 Apr, 2016, 02:46: PM
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