Advertisements
Advertisements
प्रश्न
In the given figure, O is the centre of the circle and ∠DAB = 50° . Calculate the values of xand y.
Advertisements
उत्तर
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
संबंधित प्रश्न
In Fig. 1, QR is a common tangent to the given circles, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm, then the length of QR (in cm) is :
(A) 3.8
(B) 7.6
(C) 5.7
(D) 1.9
In the given figure, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS.
A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.
The circumference of a circle is 22 cm. The area of its quadrant (in cm2) is
The radius of a circle of diameter 24 cm is _______
In the adjoining figure, Δ ABC is circumscribing a circle. Then, the length of BC is ______
A point P is 13 cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12cm. Find the radius of the circle.
If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in figure. Prove that ∠BAT = ∠ACB
If AOB is a diameter of a circle and C is a point on the circle, then AC2 + BC2 = AB2.
Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.
