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The extremities of a diagonal of a rectangle are(-4,4)and(6,-1). A circle circumscribe the rectangle and cuts an intercept AB on the y_axis . Find the area of the triangle formed by AB and the tangents to the circle at A and B.

The extremities of a diagonal of a rectangle are(-4,4)and(6,-1). A circle circumscribe the rectangle and cuts an intercept AB on the y_axis . Find the area of the triangle formed by AB and the tangents to the circle at A and B.

Grade:11

1 Answers

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17 Points
6 years ago
Here, if the diagonal is the diameter of the circle then only the rectangle can be circumscribed so the diagonal is the diameter. Now, by diametric form of equation of circle we get circle equal to x^2+y^2-2x-3y-28=0 Now, length of intercept AB=2√(f^2-c) So, we get length of intercept=11units Now in the ΔABC, where c is the centre of the circle we have base =intercept=11 and altitude=x coordinate of the centre of circle=1unit Therefore, the area of Δ=11/2 or 5.5 sq.units Now for tangents find the coordinates where the circle intersects y-axis and then the negative reciprocal of the slope of the lines AC and BC is the slope of tangents to A and B respectively and use point slope form to find tangents. Thank you,

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