Advertisements
Advertisements
प्रश्न
If ABCD is a cyclic quadrilateral in which AD || BC (In the given figure). Prove that ∠B = ∠C.
Advertisements
उत्तर
It is given that, ABCD is cyclic quadrilateral in which AD || BC
We have to prove `angleB = angle C`
Since, ABCD is a cyclic quadrilateral
So,
`angle B + angle D = 180°` and `angle A + angle C = 180°` ..… (1)
`⇒ angleB + angle A ` = 180° and `angle C + angle D = 180°` (Sum of pair of consecutive interior angles is 180°) …… (2)
From equation (1) and (2) we have
`angleB + angleD + angleB + angle A ` = 360° …… (3)
`angleA + angleC + angleC + angle D ` = 360° …… (4)
`2angleB + angleD + angleA = 2 angleC + angleA + angleD`
`2angleB = 2angleC`
`angleB = angleC`
Hence Proved
APPEARS IN
संबंधित प्रश्न
In the below fig. O is the centre of the circle. If ∠APB = 50°, find ∠AOB and ∠OAB.
In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6cm, BC=7cm and CD=4 cm. Find AD.
In two concentric circles, a chord of length 8 cm of the large circle touches the smaller circle. If the radius of the larger circle is 5 cm, then find the radius of the smaller circle.
In Fig. 8.79, PQ is a tangent from an external point P to a circle with centre O and OP cuts the circle at T and QOR is a diameter. If ∠POR = 130° and S is a point on the circle, find ∠1 + ∠2.
Find the diameter of the circle if the length of a chord is 3.2 cm and itd distance from the centre is 1.2 cm.
In figure, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at point A, then ∠BAT is equal to ______.
If a hexagon ABCDEF circumscribe a circle, prove that AB + CD + EF = BC + DE + FA.
In the following figure, if ∠OAB = 40º, then ∠ACB is equal to ______.
A circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm.
From the figure, identify a segment.
