Multiple choice

In a circle with centre O, AOC is the diameter of circle, BD is chord and meets OB and CD. If ?AOB = 1300 then ?BDC equals to-

  1. 300

  2. 250

  3. 500

  4. 600

  5. 1200
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B Correct answer
Explanation

AOC is diameter, so ∠ABC = 90° (angle in semicircle). Given ∠AOB = 130° (assuming 130°, not 1300 which is clearly a typo). ∠BOC = 180° - 130° = 50°. BD is chord meeting OB at... We need ∠BDC. In cyclic quadrilateral or using circle properties: ∠BDC = 180° - ∠BOC = 180° - 50° = 130°, but this isn't an option. Using inscribed angle theorem: ∠BDC = ∠BOC/2 = 25°.

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