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X Yand Xprime Yprimeare two parallel tan...

`X Y`and `Xprime Yprime`are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting `X Y`at A and `XprimeYprime`at B. Prove that `/_A O B\ =\ 90^o`

Text Solution

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In `/_\OPA` and `/_\OCA`
`OP=OC` (Radii of the same circle)
`AP=AC` (Tangent from point A)
`AO=AO` (Common side)
By SSS congruency, `/_\OPA` and `/_\OCA` are congruent.
Thus, `/_POA=/_COA`
Similarly, we can show
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