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, the sides AB, BC and CA of a triangle ABC, touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, then the length of BC (in cm) is ?
If AB, BC and CD are equal chords of a circle with O as centre and AD diameter, than ∠AOB =
The length of three concesutive sides of a quadrilateral circumscribing a circle are 4 cm, 5 cm, and 7 cm respectively. Determine the length of the fourth side.
In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –
(1) m(arc PR)
(2) m(arc QS)
(3) m(arc QSR)
In an equilateral triangle, prove that the centroid and center of the circum-circle (circumcentre) coincide.
Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm, and 7 cm. Find the radii of the circles.
A point P is 10 cm from the center of a circle. The length of the tangent drawn from P to the circle is 8 cm. The radius of the circle is equal to ______
If a number of circles pass through the endpoints P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.
In the following figure, O is the centre of the circle. Shade sectors OAC and OPB.
AB is a chord of a circle with centre O. AOC is diameter of circle, AT is a tangent at A.
Write answers of the following questions:
- Draw the figure using the given information.
- Find the measures of ∠CAT and ∠ABC with reasons.
- Whether ∠CAT and ∠ABC are congruent? Justify your answer.
