O is the centre of the circle calculate value of x
Answers
Answer:
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
O is the centre of the circle and ∠DAB=50
o
. Calculate the values of x and y respectively
314983
expand
Easy
Solution
verified
Verified by Toppr
Correct option is A)
□ABCD is inscribed in a circle.
So, □ABCD is cyclic quadrilateral.
⇒ ∠A+∠C=180
o
[ Sum of opposite angles in cyclic quadrilateral are supplementary ]
⇒ 50
o
+y=180
o
⇒ y=180
o
−50
o
∴ y=130
o
In △AOB,
⇒ OA=OB [ Radius of a circle ]
⇒ ∠OAB=∠OBA=50
o
[ Base angles of equal sides are also equal ] --- ( 1 )
⇒ ∠OAB+∠OBA+∠AOB=180
o
⇒ 50
o
+50
o
+∠AOB=180
o
[ From ( 1 ) ]
⇒ ∠AOB=180
o
−100
o
⇒ ∠AOB=80
o
------ ( 2 )
⇒ ∠AOB+∠BOD=180
o
[ Linear pair ]
⇒ 80
o
+x=180
o
[ From ( 2 ) ]
⇒ x=180
o
−80
o
∴ x=100
o
∴ x=100
o
and y=130
o
.