Problem: If the three points of contact of a circle inscribed in a triangle are joined, the angles of the resulting triangle:
Answer Choices:
A. are always equal to 60∘
B. are always one obtuse angle and two unequal acute angles
C. are always one obtuse angle and two equal acute angles
D. are always acute angles
E. are always unequal to each other
Solution:
∠A′=2a​,∠A=180∘−a;
​∴a=180∘−∠A.∠A′=2a​=90∘−2∠A​;∴∠A′<90∘.​
Similarly, ∠B′<90∘,∠C′<90∘.
