Question

In the figure O is the centre and AD is the diameter of the circle B and C are two points on it Angle DOB=50degree

Answer 1

Given :- In the figure O is the centre and AD is the diameter of the circle B and C are two points on it . ∠ DOB = 50° .

To Find :-

• ∠OAC = ?
• ∠BOC = ?

Solution :-

→ ∠DOB = 50° (given)

→ ∠ DOC = 50° (given)

so,

→ ∠ DOB + ∠ DOC = 50° + 50°

→ ∠ BOC = 100° (Ans.)

now,

→ ∠ DOC + ∠AOC = 180° { Linear pair angles.)

→ 50° + ∠AOC = 180°

→ ∠AOC = 180° - 50°

→ ∠AOC = 130°

now, in ∆AOC we have,

→ ∠AOC = 130°

→ AO = OC { Radius of circle.}

so,

→ ∠OAC = ∠OCA { Angle opposite to equal sides are equal in length.}

then,

→ ∠OAC + ∠OCA + ∠AOC = 180° {Angle sum property.}

→ ∠OAC + ∠OAC + 130° = 180°

→ 2∠OAC = 180° - 130°

→ ∠OAC = 50°/2

→ ∠OAC = 25° (Ans.)

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Answer 2

Answer:

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Step-by-step explanation: