Question

ABC is a triangle made in a semicircle.if AC=BC, find angle CAB​

Answer 1

Answer

⇒ In △ABC,

⇒ ∠BCA=90

o

[ Angle inscribed in semi-circle ]

⇒ AC=BC [ Given ]

∴ ∠ABC=∠CAB [ Opposite angles of equal sides are equal ]

∴ ∠CAB+∠ABC+∠BCA=180

o

∴ ∠CAB+∠CAB=90

o

=180

o

∴ 2∠CAB=180

o

−90

o

∴ 2∠CAB=90

o

∴ ∠CAB=45

o☺

Answer 2

Answer:

⇒   In △ABC,

⇒   ∠BCA=90o                [ Angle inscribed in semi-circle ]

⇒  AC=BC                       [ Given ]

∴    ∠ABC=∠CAB         [ Opposite angles of equal sides are equal ]

∴    ∠CAB+∠ABC+∠BCA=180o

∴    ∠CAB+∠CAB=90o=180o

∴    2∠CAB=180o−90o

∴    2∠CAB=90o

∴   ∠CAB=45o