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Circles — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSCircles1 Mark
Question
If A , B, C are three points on a circle with centre O such that $\angle\text{AOB} = 90^\circ$ and $\angle\text{BOC} = 120^\circ,$ then $\angle\text{ABC} =$
✓

Answer

  1. 75°
    Solution:

    $\angle\text{AOC}=\angle\text{AOB}+\angle\text{BOC}$
    $=90^\circ+120^\circ=210^\circ$
    $\angle\text{COA}=360^\circ-210^\circ=150^\circ$
    If arc $\widehat{\text{COA}}$ makes 150° at centre, then it will make half angle of the centre at circumference.
    $\Rightarrow\angle\text{CBA}$ or $\angle\text{ABC}=\frac{150^\circ}{2}=75^\circ$

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