Circle tangent!

Geometry Level pending

Find the angle between the two tangents from the origin to the circle ( x − 7 ) 2 + ( y + 1 ) 2 = 25 (x-7)^2+(y+1)^2=25 .

π 2 \frac{\pi}{2} π 6 \frac{\pi}{6} π 3 \frac{\pi}{3} π 4 \frac{\pi}{4}

Sahil Silare by Sahil Silare , 20, India

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1 solution

Tapas Mazumdar
Dec 17, 2016

Equation of director circle for this circle is

( x − 7 ) 2 + ( y + 1 ) 2 = 2 r 2 = 50 {(x-7)}^2 + {(y+1)}^2 = 2r^2 = 50

Putting ( 0 , 0 ) (0,0) in the equation, we find that it lies on the director circle. Since, tangents drawn from any point on the director circle of a circle to the given circle are always perpendicular. So, the angle between the tangents will be π 2 \boxed{\dfrac \pi2} .

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Nice one bro!

Sahil Silare - 4 years, 6 months ago

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Thanks bro! :)

Tapas Mazumdar - 4 years, 6 months ago

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