Advertisements
Advertisements
प्रश्न
In the given figure, O is the centre of the circle. If ∠CEA = 30°, Find the values of x, y and z.
Advertisements
उत्तर
It is given that, O is the centre of the circle and `angle AEC = 30°`
We have to find the value of x, y and z.
Since, angle in the same segment are equal
So `angle AEC = angle ADC = 30°`
And z = 30°
As angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Since `angle AOC = 2 angle ADC`
Then,
y = 2z
= 2 × 30°
= 60°
Since, the sum of opposite pair of angles of a cyclic quadrilateral is 180°.
z + x = 180°
x = 180° − 30°
= 150°
Hence,
x = 150°, y = 60° and z = 30°
APPEARS IN
संबंधित प्रश्न
true or false
A chord of a circle, which is twice as long is its radius is a diameter of the circle.
In the given figure, O is the centre of the circle. If ∠AOB = 140° and ∠OAC = 50°; find:
- ∠ACB,
- ∠OBC,
- ∠OAB,
- ∠CBA.
In the given figure, PQ is chord of a circle with centre O an PT is a tangent. If
∠QPT = 60°, find the ∠PRQ.
Two circles touch internally. The sum of their areas is 116 π cm2 and the distance between their centres is 6 cm. Find the radii of the circles ?
In the given figure, O is the centre of the circle. If ∠BOD = 160°, find the values of x and y.
In following fig. ABC is an equilateral triangle . A circle is drawn with centre A so that ot cuts AB and AC at M and N respectively. Prove that BN = CM.
ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.
Construct a triangle ABC with AB = 4.2 cm, BC = 6 cm and AC = 5cm. Construct the circumcircle of the triangle drawn.
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.
From the figure, identify three radii.
