Question

in the figure AB = 6 cm,
$< aob = 60\%$
1. find OAB
2. find OBA
3. find the radius of the circle


plzz sent the correct answer ​

Answer 1

Here,

OA = OB = radius of triangle

so, <OAB = <OBA = k (let)

now, <AOB =60⁰

but we know <OAB + <OBA + <AOB = 180⁰

=> k + k + 60⁰ = 180⁰

=> 2k = 180⁰ - 60⁰ = 120⁰

=> k = 120/2 = 60⁰

so, 1. <OAB =60⁰

2. <OBA =60⁰

And as it is an equilateral triangle so, OA = AB = BC =6cm

(ans)

Answer 2

Given :- in the figure AB = 6 cm, ∠AOB = 60° .

To Find :-

1. ∠OAB ?
2. ∠OBA ?
3. Radius of the circle. ?

Solution :-

from image , we have ,

• OA = OB = radius of circle.

So, in ∆OAB ,

→ OA = OB

→ ∠OAB = ∠OBA { angle opposite to equal sides are equal. }

then, by angle sum property ,

→ ∠OAB + ∠OBA + ∠AOB = 180°

→ 2∠OAB = 180° - 60°

→ 2∠OAB = 120°

→ ∠OAB = ∠OBA = 60° (Ans.)

Therefore,

• ∆OAB is an Equaliteral ∆ .

Hence,

• All sides of an Equaliteral ∆ are equal in length .
• Radius of circle = AB => 6 cm. (Ans.)

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