Angle in an isosceles triangle formed by circle radii

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Geometry

In a circle of radius 6 cm, arc AB makes an angle of 114° with centre of the circle O. What is angle ABO?

  1. A.

    23°

  2. B.

    42°

  3. C.

    38°

  4. D.

    33°

Answer

D

Explanation

In △AOB\triangle AOB, OA=OB=6 cmOA = OB = 6\text{ cm} (radii of circle). Thus △AOB\triangle AOB is isosceles with ∠OAB=∠ABO\angle OAB = \angle ABO. Sum of angles in △AOB=180∘\triangle AOB = 180^\circ. ∠AOB+2∠ABO=180∘  ⟹  114∘+2∠ABO=180∘  ⟹  ∠ABO=180∘−114∘2=33∘\angle AOB + 2 \angle ABO = 180^\circ \implies 114^\circ + 2 \angle ABO = 180^\circ \implies \angle ABO = \frac{180^\circ - 114^\circ}{2} = 33^\circ.

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