CBSE Class 9 Answered
A point O is taken inside an equilateral four sided figure ABCD such that its distances from the angular points D and B are equal. Show that AO and OC are in one and the same straight line.![](https://images.topperlearning.com/topper/questions/8175_image014.jpg)
![](https://images.topperlearning.com/topper/questions/8175_image014.jpg)
Asked by Topperlearning User | 10 Aug, 2017, 12:36: PM
In
AOD and
AOB
![](https://images.topperlearning.com/topper/questions/8175_image004.gif)
![](https://images.topperlearning.com/topper/questions/8175_image004.gif)
AD = AB (given)
AO =AO (common side)
OD = OB (given)
![](https://images.topperlearning.com/topper/questions/8175_image015.gif)
![](https://images.topperlearning.com/topper/questions/8175_image004.gif)
![](https://images.topperlearning.com/topper/questions/8175_image007.gif)
![](https://images.topperlearning.com/topper/questions/8175_image004.gif)
![](https://images.topperlearning.com/topper/questions/8175_image015.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
Similarly,
DOC ![](https://images.topperlearning.com/topper/questions/8175_image007.gif)
BOC (SSS congruence rule)
![](https://images.topperlearning.com/topper/questions/8175_image004.gif)
![](https://images.topperlearning.com/topper/questions/8175_image007.gif)
![](https://images.topperlearning.com/topper/questions/8175_image004.gif)
![](https://images.topperlearning.com/topper/questions/8175_image015.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
2
AOD + 2
DOC = 360o
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
![](https://images.topperlearning.com/topper/questions/8175_image005.gif)
Hence, AO and OC are in one and the same straight line.
Answered by | 10 Aug, 2017, 14:36: PM
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