CBSE Class 9 Answered
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, 21:14: PM
The question should be :
AC is the diameter of the circle whose centre is O. AB and CD are parallel chords of a circle. Prove that AB=CD
Solution:
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/34c53c4e0f1cada0ed74a7b9c2382f885e29260e65d066.58495499ATE.png)
In triangles ABC and ACD,
![angle A B C equals angle A D C space... space left square bracket E a c h space 90 degree space a s space A C space i s space t h e space d i a m e t e r right square bracket
angle B A C equals angle D C A space... space left square bracket A l t e r n a t e space i n t e r i o r space a n g l e s right square bracket
A C equals A C space.... space left square bracket C o m m o n space s i d e right square bracket
therefore triangle A B C approximately equal to triangle C D A space... space left square bracket U sin g space A A S space c o n g r u e n c y space c r i t e r i a right square bracket
rightwards double arrow A B equals C D](https://images.topperlearning.com/topper/tinymce/cache/b1b5ddc0c350bcd225c87806e6042d7c.png)
Answered by Renu Varma | 23 Jan, 2020, 10:27: AM
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