In `DeltaABC, angleC=2angle A` and AC=2BC. Then which of the following is/are True ?

Options

A. Angles A,B,C are in arithmetic progression
B. Angles A,C,B are in arithmetic progression
C. `Delta ABC` is a right angled isosceles triangle
D. `BC^(2)+CA^(2)+AB^(2)=8R^(2)`, where R is the circum-radius of `Delta ABC`

Answer

B, D

Explanation

`angle C=2 angle A` and b = 2a
`rArr sin B = 2 sin A`
`rArr sin (A+C)=2 sin A`
`rArr sin 3A=2 sin A`
`rArr 3-4 sin^(2)A=2`
`rArr sin A=(1)/(2)rArr A=30^(@)`
`therefore C=60^(@), B=90^(@)`
`rArr a^(2)+b^(2)+c^(2)=8R^(2)`
`rArr sin^(2)A+sin^(2)B+sin^(2)C=2`