Mathematics - Circle Question with Solution | TestHub
For Q63-65: S1: x² + y² - 2x = 0 and S2: x² + y² + 6x = 0. Their two direct common tangents touch S1 at A, B and S2 at C, D; they meet at P and cut a transverse common tangent at Q, R respectively.
. Their two direct common tangents touch at at , meet at , and cut a transverse common tangent at respectively. Find, in order, the centre of the circle through and the centre of a circle touching internally.
Options:
Answer:
Solution:
The source diagram and coaxial pencil give the four-point circle centre . The midpoint of the extreme endpoints of is , the claimed centre for the internally tangent circle. Verify the intended meaning of touching both circles internally; the smaller lies inside a circle of centre ( ) radius 4 , and the larger is internally tangent to it.
