Question

In the figure, YX−→− is a tangent to circle O at point X. mXB=52∘ mXA=104∘ What is the measure of ∠XYA ?

Answer 1

`m/_XYA=26^@`

Explanation:

Let us join `OX`, `OA`, `OB` and `XA`.

As measure of arc `XA=104^@`, `/_XOA=104^@` and

`m/_XBA=1/2xx104=52^@`

Further, as measure of arc `XB=52^@`, `m/_XOB=52^@` and

and `m/_BXY=1/2xx52^@=26^@`

Hence, `m/_XYA=m/_XYB=m/_XBA-m/_BXY=52^@-26^@=26^@`