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# If the lines shown in the picture touch the circle with center O only

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Re: If the lines shown in the picture touch the circle with center O only [#permalink]
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mafuz wrote:
Hi! how D creates two right angle. Can anyone explain. I did not understand above explanation as it said ...figure is symmetrical to CDO..

mafuz

This can be said by applying the properties of a triangle
Consider triangle ACO and BCO
Here AO=OB(BOTH ARE RADIUS OF CIRCLE WITH CENTRE O); Angle CAO and Angle CBO are 90 degree; CA=CB(both are tangent)

So we can say by property SAS that triangle CAO is congruent to Triangle CBO

Now, consider triangle ADO and Triangle BDO
Here, AO=BO(Radius); angle AOD = angle BOD(using congruent condition of traingle ACO and BCO); OD=OD(Same side)
So, traingle ADO and BDO are congruent

Now since ADC is a chord, and angle ADO and BDO are same; we can say they are 90 degree

Hope this helps!
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Re: If the lines shown in the picture touch the circle with center O only [#permalink]
Thanks a lot aviral
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Re: If the lines shown in the picture touch the circle with center O only [#permalink]
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Re: If the lines shown in the picture touch the circle with center O only [#permalink]
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