| Direction (Q. Nos. 90) For the following questions. Choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. |
| Consider the equation of circle is \[S={{x}^{2}}+{{y}^{2}}={{a}^{2}}\] |
| Statement I The chord of contact of tangent from these points A, B, C to the circle S are concurrent, then A, B,C will be collinear. |
| Statement II A, B, C always lies on the normal to the circle S. |
A) Statement I is true/ Statement II is also true and Statement II is the correct explanation of Statement I.
B) Statement I is true. Statement II is also true and Statement II is not the correct explanation of Statement I.
C) Statement I is true. Statement II is false.
D) Statement I is false. Statement II is true.
Correct Answer: C
Solution :
Equation of chord of contact from \[A({{x}_{1,}}{{y}_{1}})\] \[B({{x}_{2}},\,{{y}_{2}})\] and \[C({{x}_{3}},\,{{y}_{3}})\] is \[x{{x}_{1}}+y{{y}_{1}}-{{a}^{2}}=0\] \[x{{x}_{2}}+y{{y}_{2}}-{{a}^{2}}=0\] and \[x{{x}_{3}}+y{{y}_{3}}-{{a}^{2}}=0\] i.e., A, B and C are collinear.
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