the figure AB = 6 cm , < AOB = 60°
a) Find < OAB .
b) Find < OBA .
c) Find the radius of the circle .
with step by step explanation.
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Answered by
2
Step-by-step explanation:
As we know that the sum of all interior angle is 180 then,
given,
OA=OB(radius)
then,
triangle AOB is Isoceles triangle
then,
<OBA=<OAB
< OAB + < OBA + <AOB = 180
2<OAB+<AOB =180
2<OAB=180-60
2<OAB=120
<OAB=60°
Therefore the value of <OAB =<OBA=60°
Answered by
4
Step-by-step explanation:
Given: A circle with center O.
< AOB = 60°
AB = 6cm
To Find: (I) < OAB
(ii) < OBA
(iii) Find the radius of the circle
Solution:
OA = OB ( Radius of of the circle ) --------- ( 1 )
therefore, < OAB = < OBA
[ Angles opposite to equal sides of a ∆ are equal ]
- < AOB + < OAB + OBA = 180°
- < AOB = 60° [Given]
- 60° + < OAB + < OAB = 180°
[ < OAB = < OBA ]
- 2< OAB = 180 - 60
- < OAB = 120/ 2
- < OAB = 60°
Therefore, < OAB = 60° = OBA
now, ∆AOB is an equilateral ∆. --------( 2 )
According to equation ( 1 ) and ( 2 )
AB = OA = OB = 6cm
Therefore,
(i) < OAB = 60°
(ii) < OBA = 60°
(iii) radius of the circle = 6cm
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