A circle has a radius of 1. Two tangents with gradients 2 and -2 meet the circle as shown below. The purple line goes through the diameter and meets one of the tangents on the circumference of the circle.
Find the area of the triangle outlined in red to 3 decimal places.
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The length of the red part of the blue line is given by c o t ( a r c t a n ( 2 1 )) = 2
The angle between the tangents can be found using 1 8 0 − 2 a r c t a n ( 2 ) which is roughly equal to 5 3 . 1 3 0 . . .
The red part of the purple line can be given by 2 a r c t a n ( 5 3 . 1 3 0 . . . ) = 3 8
The formula for the area of a triangle 2 1 b h can then be used to get a result of 3 8 , which is 2 . 6 6 7 to 3dp.