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Standard IX
Mathematics
SSS Criteria for Congruency
O is the cent...
Question
O is the centre of the circle. If
∠
BAC=
50
∘
, find ∠OBC.
___
Open in App
Solution
Given: In a circle with centre at O
BAC =
.
To find:
OBC = ?
Procedure:
∠ BOC = 2
BAC = 2(
) =
100
(Arc BC subtends
BOC at the centre and
BAC at remaining part of circle)
In
△
OBC, OB = OC = radius
OBC =
OCB (Opposite angles of equal sides of a Δ)
Now,
OBC +
OCB +
BOC =
180
(Sum of angles in a triangle)
=
–
2
80
∴
40
Answer:
angle OBC is 30°
pls check the diagram once
let point of intersection be M
angle OAB = angle OCD (angle in same segment)
angle O is 90
by angle sum property 90+60+B =180
angle ODA= 180 - 150 = 30°
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Answers & Comments
Step-by-step explanation:
Find solutions
CameraIcon
MyQuestionIcon
Byju's Answer
thumbs-up
Standard IX
thumbs-up
Mathematics
thumbs-up
SSS Criteria for Congruency
thumbs-up
O is the cent...
Question
O is the centre of the circle. If
∠
BAC=
50
∘
, find ∠OBC.
___
Open in App
Solution
Given: In a circle with centre at O
∠
BAC =
50
∘
.
To find:
∠
OBC = ?
Procedure:
∠
BAC =
50
∘
∠ BOC = 2
∠
BAC = 2(
50
∘
) =
100
∘
(Arc BC subtends
∠
BOC at the centre and
∠
BAC at remaining part of circle)
In
△
OBC, OB = OC = radius
∠
OBC =
∠
OCB (Opposite angles of equal sides of a Δ)
Now,
∠
OBC +
∠
OCB +
∠
BOC =
180
∘
(Sum of angles in a triangle)
∠
OBC +
∠
OCB +
100
∘
=
180
∘
∠
OBC +
∠
OBC =
180
∘
–
100
∘
2
∠
OBC =
80
∘
∴
∠
OBC =
40
∘
Verified answer
Answer:
angle OBC is 30°
Step-by-step explanation:
pls check the diagram once
let point of intersection be M
angle OAB = angle OCD (angle in same segment)
angle O is 90
by angle sum property 90+60+B =180
angle ODA= 180 - 150 = 30°