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In the figure, the radius of a circle wi...

In the figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A and AB is 6 cm. Answer the following questions.
What is the measure of `/_ABC?` Why?.

Text Solution

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The correct Answer is:
`/_ABC=45^(@)`
In `triangle ABC`,
`CA=AB " " "........."(" Each is the length 6 cm ")`
`:./-ABC+/_ACB"......."(" Isosceles triangle theorem ")`
Let `/_ABC=/_ACB=x^(@)`
In `triangle ABC`,
`/_CAB+/_ABC+/_ACB=180^(@)`
`"........."(" Sum of all angles of a triangle is " 180^(@))`
`:.90^(@)+x^(@)+x^(@)=180^(@)`
`:.2x=180^(@)-90^(@)`
`:.2x=90^(@)`
`:.x^(@)=(90^(@))/(2)" " :.x^(@)=45^(@)`
`:./_ABC=45^(@)`.
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