Question

Circle tangent question?

Answer 1

Let K the tangent RST intersects the smaller circle at K.

Construction

`O,Q;O,SandQ,T` are joined.

Given ST is tangent to the circle of center O and `angle QST=46^@`

We have alternate`angleQPS=angle QST=46^@`

Hence central `angleQOS=2angleQPS=92^@`

Now in cyclic quadrilateral `OQTS`

Sum of opposite angles

`angleQOS+angleQKS=180^@`

`=>92^@+angleQKS=180^@`

`=>angleQKS=180^@-92^@=88^@<90^@`

So `angleQKS<90^@` can not be semicircular angle.

Hence `SQ` is not a diameter.