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 | 14th Jan, 2020, 09:14: PM

Expert Answer:

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:
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

Answered by Renu Varma | 23rd Jan, 2020, 10:27: AM