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प्रश्न
In the adjoining figure ‘O’ is the center of the circle, ∠CAO = 25° and ∠CBO = 35°. What is the value of ∠AOB?
पर्याय
120°
110°
55°
Data insufficient
MCQ
उत्तर
120°
Explanation:
In ΔAOC,
OA = OC ................. (radii of the same circle)
∴ ΔAOC is an isosceles triangle.
→ ∠OAC = ∠OCA = 25° .................(base angles of an isosceles triangle )
In ΔBOC,
OB = OC ................. (radii of the same circle)
∴ ΔBOC is an isosceles triangle
→ ∠OBC = ∠OCB = 35° .............. (base angles of an isosceles triangle )
∠ACB = 25° + 35°= 60°
∠AOB = 2 × ∠ACB .............. (the angle at the center is twice the angle at the circumference)
= 2 × 60°
= 120°
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