Advertisements
Advertisements
Question
In the given figure, O is the centre of the circle and ∠DAB = 50° . Calculate the values of xand y.
Advertisements
Solution
It is given that, O is the centre of the circle and \[\angle DAB = 50° \]
We have to find the values of x and y.
ABCD is a cyclic quadrilateral and `angle A + angle C = 180°`
So,
50° + y = 180°
y = 180° − 50°
y = 130°
Clearly Δ OAB is an isosceles triangle with OA = OB and `angle OBA = angle OAB`
Then, `angle OBA + angleOAB + angle AOB = 180°`
`angleAOB = 180° - ( 50° + 50° ) ` (Since `angleOBA = angle OAB = 50°` )
So, `angleAOB = 80°`
x + `angle AOB ` = 180° (Linear pair)
Therefore, x = 180° − 80° = 100°
Hence,
x = 100° and y = 130°
APPEARS IN
RELATED QUESTIONS
Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle.
In figure 1, O is the centre of a circle, PQ is a chord and PT is the tangent at P.
If ∠POQ = 70°, then ∠TPQ is equal to
In the given figure, ΔABC is an equilateral triangle. Find m∠BEC.
In the given figure, if ABC is an equilateral triangle. Find ∠BDC and ∠BEC.
Draw a circle of radius of 4.2 cm. Mark its center as O. Takes a point A on the circumference of the circle. Join AO and extend it till it meets point B on the circumference of the circle,
(i) Measure the length of AB.
(ii) Assign a special name to AB.
Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).
| radius (r) | diameter (d) | Circumference (C) |
| 1760 cm |
The ______________ is the longest chord of a circle
In the adjoining figure ‘O’ is the center of the circle, ∠CAO = 25° and ∠CBO = 35°. What is the value of ∠AOB?
O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.
Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.
