This question was uploaded on 13/10/21 on social media accounts.
Semicircle inscribed in a quarter circle such that its corners are on the quarter circle and it touches on one side of the quarter circle and also touches a chord perpendicular to the side of quarter circle.
Solution:
\[x^2=(r+1)^2+r^2=R^2-r^2\]
By intersecting chord theorem at point P:
\[(R-1)(R+1)=(r+2)^2\]
After solving these two equations, we get:
\[r = 2\]
(R will be canceled from both sides while solving these equations)
\[Area = \frac\pi2r^2=2\pi\]
Puzzle related to Geometry, Area, Circle.
