This question was uploaded on 08/09/21 on social media accounts.
A semicircle and an equilateral triangle are drawn such that the semicircle starts from one vertex of the triangle, passing through one side, touches the second side, and ends on the third side. Two lines are drawn by using the Initial point of the circle, intersection point, tangential point. Find inclination on the first line and angle between two lines.
Solution:
For angle α:
Explanation:
The explanation for right angle:
The point is a tangential point.
The explanation for α = 30/2:
Inscribed angle theorem, 30 is at the center so that it will make half of 30 on any point of the circle.
For β:
1)
This solution is similar to the solution for α.
How β is the same?
Both are on the same arc of the triangle.
2)
The explanation for right angle:
An angle inscribed in a semicircle is always 90.
Puzzle based on Geometry, Triangle, Circle, Angle.
