Question

AA1, BB1 and CC1 are the medians of triangle ABC whose centroid is G. If points A, C1, G and B1 are concyclic, then​

Answer 1

AA1, BB1 and CC1 are the medians of triangle ABC whose centroid is G.

Since A, C1, G and B1 are concyclic, then

1. BG⋅BB1 = BC1⋅BA

2. 2/3 ( BB1)^2 = (c/2).c

3. (2/3).(1/4).(2a^2 + 2c^2 - b^2 ) =

c^2/2

4. 2a^2 + 2c^2 - b^2 = 3c^2

5. b^2 + c^2 = 2a^2

Answer 2

Answer:

2b^2=a^2+c^2 ........