This question was uploaded on 19/09/21 on social media accounts.
A circle is drawn using two perpendicular equal lines such that the circle touches the end of both lines and the circle is also passing through any point on the lines. Let the distance between the end of one line and the intersection of the circle with the other line is 2 then find the area of the circle.
Solution 1:
Radius:
\[2r^2=2^2\]
\[\Rightarrow r=\sqrt2\]
Area:
\[A = \pi r^2 = 2\pi\]
Explanation:
1) 45° is due to the same length of both lines and the angle between them is 90°.
2) The angle between two lines with radius r is 90° due to the inscribed angle theorem on the yellow chord.
Solution 2:
Here, (1) and (2) are similar triangles and the angle between the two lines is 90°.
By this angle between both yellow lines is 90°.
That means they are made on a diameter.
Diameter:
\[d^2=2(2^2)\]
\[\Rightarrow d=2\sqrt2\]
Radius:
\[r=\sqrt2\]
Area:
\[A = \pi r^2 = 2\pi\]
