A-b is the mid point of the chord AB of the circle x 2- y 2- r 2- The tangent at A - B meet a C- then area of - ABCA- a2-b2-r23-2-a2-b2B- a2-b2-r23-2-a2-b2C- r2-a2-b23-2-a2-b2D- a2-b2-r23-2-a2-b2

The correct option is C Equation of the chord AB having (a,b) as M.P.S_1 = S_11⇒ ax +by (a^2+b^2)=0 chord length = 2 √(r^2 a^2 b^2) c= ( ar^2/a^2+b^2,br^2/ ...

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Standard XII

Mathematics

Direct Common Tangent

a,b is the mi...

Question

(a,b) is the mid point of the chord $¯ A B$ of the circle $x^{2} + y^{2} = r^{2}$ . The tangent at A,B meet a C. then area of $Δ A B C$

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Solution

The correct option is B

Equation of the chord AB having (a,b) as $M . P . S_{1} = S_{11} \Rightarrow a x + b y - (a^{2} + b^{2}) = 0$ chord length = $2 \sqrt{r^{2} - a^{2} - b^{2}} c = (\frac{- a r^{2}}{a^{2} + b^{2}}, \frac{b r^{2}}{a^{2} + b^{2}}) h = \frac{r^{2} - a^{2} - b^{2}}{\sqrt{a^{2} + b^{2}}} A r e a = \frac{1}{2} \times b \times h$

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(a,b) is the mid point of the chord ¯AB of the circle x2+y2=r2. The tangent at A,B meet a C. then area of ΔABC

The correct option is B Equation of the chord AB having (a,b) as M.P.S1=S11⇒ax+by−(a2+b2)=0 chord length = 2√r2−a2−b2c=(−ar2a2+b2,br2a2+b2)h=r2−a2−b2√a2+b2Area=12×b×h

(a,b) is the mid point of the chord $¯ A B$ of the circle $x^{2} + y^{2} = r^{2}$ . The tangent at A,B meet a C. then area of $Δ A B C$