This question was uploaded on 16/10/21 on social media accounts.
Two semicircles on a straight line and a common tangent to them. Find the area of the triangle formed by the tangent and common point of both semicircles.
Solution:
Here,
\[x = a\cdot\tan\theta\]
\[y = \frac b{\tan\theta}\]
Blue triangle is right-angled triangle:
\[\Rightarrow Area=\frac{xy}2=\frac{ab}2\]
Click here to get the proof of the blue triangle is the right-angled triangle and why those angles in the figure are the same.
