Tangents TP , TQ are drawn from T to x 2 + y 2 = 4 . If T lies on 3 x + 4 y − 12 = 0 , find the area bounded by the locus of the circumcentre of △ TPQ and the coordinate axes.

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If T = ( x 1 ​ , y 1 ​ ) , the circumcircle of TPQ has centre ( x 1 ​ /2 , y 1 ​ /2 ) . Its locus is 3 x + 4 y = 6 , whose intercept triangle has area 2 1 ​ ( 2 ) ( 3/2 ) = 3/2 .

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