Dare2Solve | Circle inside a semicircle passing through center of the semicircle

This question was uploaded on 01/12/21 on social media accounts.

Solution 1:

Here y is same due to angle on same arc.

45 - y = 180 - (45 + y)

tan(45 + y) = 3

So, tan(x) = -3

Solution 2:

Diameter is drawn in the smaller circle.

tan(x - 90) = 1/3

tan(90 - x) = - 1/3

cot(x) = - 1/3

So, tan(x) = - 3