Multiple choice

In a cirlce of centre O, AB is a diameter and CD is a chord to the circle. ∠AOD = 106o then what is the value of ∠BCD. O वृत्त वाले केन्द्र में, AB एक व्यास है और CD वृत्त पर जीवा है। ∠AOD = 106o तो ∠BCD का मान क्या है?

  1. 53o

  2. 43o

  3. 40o

  4. 37o
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D Correct answer
Explanation

AB is a diameter, so ∠ABC = 90° (angle in semicircle). Given ∠AOD = 106° (central angle), arc AD = 106°. ∠ABD = 106°/2 = 53° (inscribed angle on same arc). In right triangle ABC: ∠ABC + ∠BCD = 90°, so ∠BCD = 90° - 53° = 37°.

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