Question

B. Three girls A, B and C are standing on the circumference of a circle with radius 10 cm and centre at point O.
If the distance between A and B = distance between B and C = 16 cm, find the distance between A and C.
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Answer 1

Step-by-step explanation:

Given that: ∠OAC=53°

∠CBO=32°

Consider △ACO:

AO=CO (radius of circle)

Thus, ∠ACO=∠OAC=53° (angles opposite to equal sides are equal)

∠AOC=180°−53°−53°=74° (Sum of three angles of a triangle is 180°)

Similarly in △BCO:

BO=OC

Hence, ∠OBC=∠OCB

And ∠COB=180°−32°−32°=116°

Reflex∠AOB=∠AOC+∠COB=74°+116°=190°

Thus ∠AOB=360°−reflex∠AOB

∠AOB=360°−190°=170°

Answer: ∠AOB=170°