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In DeltaABC, angleC=2angle A and AC=2BC....

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

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`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`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`
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