Given, circle (x−a)2+y2=a2 and x2+(y−a)2=a2 Common chord of circle is (x−a)2−x2+y2−(y−a)2=0
⇒(x−a−x)(x−a+x)+(y+y−a)(y−y+a)=0
⇒(2x−a)−(2y−a)=0⇒x−y=0
End point of chord is (0,0),(a,a) Mid-point of chord is (‌
a
2
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a
2
) ∴(I) is true Length of common chord is √a2+a2=√2a Intersection point of common chord is (0,0) and (a,a) Distance from centre to common chord is