1.

In the given, figure , O is the centre of the circle and AD is a tangent to the circle at.A if `angle CAD =55^@` and `angle ADC=25^@`, then find `angle ABO`.

Answer» (i) Join OA and OC.
(ii) `angle ACD =180^@-80^@=100^@`.
(iii) `angle ACB and angle ACD ` are supplementary.
`rArr angle ACB +angle ACD =180^@`.
`rArr angle ACB =80^@`
(iv) `angle AOB =2angle ACB.rArr AOB =2xx80^@=160^@`
(v) Now, In `Delta AOB`,
`angle O+angle A+angle B=180^@`
`160^@+x+x=180^@`
`2x=20^@`
`x=10^@`
`therefore` Hence, option (a) is the correct answer.


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