SSC CGL 10 Aug 2017 Shift 1 Paper

Question : 66 of 100

Marks: +1, -0

Circumcentre of ΔABC is O. If ∠BAC =75° and ∠BCA =80°, then what is the value (in degree) of ∠OAC ?

Solution:

∠BAC = 75°

∠BCA = 80°⇒ ∠ABC

= 1 8 0 °-7 5 °-8 0 °

∴ ∠ABC = 25°
⇒ ∠AOC =2 × ∠ABC =2 × 25°
∠AOC = 50°
∵ AO = OC = radius
∴ ∠OAC = ∠OCA
⇒ ∠AOC + ∠OAC + ∠OCA = 180°
⇒ 50°+ ∠OAC + ∠OAC =180°
⇒ 2∠OAC =130°
∴ ∠OAC =65°

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