cmi-entrance 2022 QB3

cmi-entrance · India · ugmath_23may 14 marks Sine and Cosine Rules Multi-step composite figure problem

[14 points] In $\triangle A B C , \angle B A C = 2 \angle A C B$ and $0 ^ { \circ } < \angle B A C < 120 ^ { \circ }$. A point $M$ is chosen in the interior of $\triangle A B C$ such that $B A = B M$ and $M A = M C$. Prove that $\angle M C B = 30 ^ { \circ }$.
Hint (use this or your own method): Draw a suitable segment $C D$ of appropriate length making an appropriate angle with $C A$.

[14 points] In $\triangle A B C , \angle B A C = 2 \angle A C B$ and $0 ^ { \circ } < \angle B A C < 120 ^ { \circ }$. A point $M$ is chosen in the interior of $\triangle A B C$ such that $B A = B M$ and $M A = M C$. Prove that $\angle M C B = 30 ^ { \circ }$.

Hint (use this or your own method): Draw a suitable segment $C D$ of appropriate length making an appropriate angle with $C A$.

Paper Questions

QA1 QA10 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB2 QB3 QB4 QB5 QB6