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  • In Figure 3, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting PQ at A and RS at B. Prove that 

In Figure 3, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting PQ at A and RS at B. Prove that \angle AOB = 90\degree

 

 

 
 
 
 
 

Answers (1)

In \Delta AOD and \Delta AOC

    OD = OC    (radius of circle)

    OA = OA    (common side)

    AD = AC    (tangent from same/common point)

    \angle D = \angle C = 90\degree    (tangent tot the circle)

So, by SAS,

        \Delta AOD \cong \Delta AOC

    \Rightarrow \angle 1 = \angle 2

Similarly, \angle 4 = \angle 3

\Rightarrow \angle 1 + \angle 4 =\angle 2 + \angle 3 = \frac{1}{2}(180\degree)

\Rightarrow\angle 2 + \angle 3 = 90\degree   

So from \Delta BOC

    \angle AOB = 90\degree

Posted by

Safeer PP

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