CBSE Class 9 Answered
AB is chord of a circle with centre O. Let P and T be two points on the circumpherence such that < APB # < ATB and < APB = 80 degree then what is the value of < ATB.
![question image](http://images.topperlearning.com/topper/new-ate/top_mob16712933761095164443IMG-20221217-WA0002.jpg)
Asked by sdmbotch1123 | 17 Dec, 2022, 21:39: PM
Given: AB is a chord to the circle with centre O
Since, P and T are two points on the circumference of the circle such that angle APB not equal to angle ATB.
So, we can say that P and T can't be on the same side of the segment AB.
We have the following figure:
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/320d472180ddb4c97268871b47e0951f639ff1f18643c3.63100375IMG20221219103610.jpg)
Here, APBT is a cyclic quadrilateral
We know that the opposite angles of a cyclic quadrilateral are supplementary i.e. thier sum if 180o.
![rightwards double arrow angle APB plus angle ATB equals 180 to the power of straight o
rightwards double arrow angle ATB equals 180 to the power of straight o minus angle APB
rightwards double arrow angle ATB equals 180 to the power of straight o minus 80 to the power of straight o
rightwards double arrow angle ATB equals 100 to the power of straight o](https://images.topperlearning.com/topper/tinymce/cache/2f9d6a591dcb5313db600fb83115e4e3.png)
Answered by Renu Varma | 19 Dec, 2022, 10:41: AM
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