cmi-entrance 2017 QA6

cmi-entrance · India · ugmath 4 marks Sine and Cosine Rules Circumradius or incircle radius computation
Consider the following construction in a circle. Choose points $A, B, C$ on the given circle such that $\angle ABC$ is $60^\circ$. Draw another circle that is tangential to the chords $AB$, $BC$ and to the original circle. Do the above construction in the unit circle to obtain a circle $S_1$. Repeat the process in $S_1$ to obtain another circle $S_2$. What is the radius of $S_2$? 
Consider the following construction in a circle. Choose points $A, B, C$ on the given circle such that $\angle ABC$ is $60^\circ$. Draw another circle that is tangential to the chords $AB$, $BC$ and to the original circle.\\
Do the above construction in the unit circle to obtain a circle $S_1$. Repeat the process in $S_1$ to obtain another circle $S_2$. What is the radius of $S_2$?
Paper Questions
QA1 QA10 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB2 QB3 QB4 QB5 QB6