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Tangents and normal from a point (3, 1) to circle C whose equation `x^(2) + y^(2) - 2x - 2y + 1 = 0` Let the points of contact of tangents be `T_(i)(x_(i),(y_(i)),` where `I = 1, 2` and feet of normal be `N_(1)` and `N_(2)( N_(1) " is near" P)` Tangents ared drawn at `N_(1) and N_(2)` and normals are drawn at `T_(1) and T_(2)`

A

`x_(1) + x_(2) + y_(1) + y_(2) = 5`

B

`x_(1)x_(2)y_(1)y_(2) = -(9)/(16)`

C

Normal at `T_(1)` and tangents at `T_(2) and N_(2)` are concurrent

D

Circle is incircle of the triangle formed by tangents from P and tangent at `N_(2)`

Text Solution

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The correct Answer is:
A, C, D
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