Advertisements
Advertisements
प्रश्न
ABCD is a cyclic trapezium with AD || BC. If ∠B = 70°, determine other three angles of the trapezium.
उत्तर
If in cyclic quadrilateral `angle B = 70°` , then we have to find the other three angles.
Since, AD is parallel to BC, So,
`angleB + angleA = 180 ` (Alternate interior angles)
`70 + angleA = 180`
`⇒ angle A = 180 - 70 = 110°`
Now, since ABCD is cyclic quadrilateral, so
`angle A + angle C = 180`
`⇒ 110 + angle C = 180`
`⇒ angle C = 180 - 110 = 70°`
And,
`angle B + angleD = 180`\
`⇒ 70 + angleD = 180`
`⇒ angleD = 180 - 70 = 110°`
APPEARS IN
संबंधित प्रश्न
A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.
In the given figure, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.
Prove that a cyclic parallelogram is a rectangle.
Let the vertex of an angle ABC be located outside a circle and let the sides of the angle intersect equal chords AD and CE with the circle. Prove that ∠ABC is equal to half the difference of the angles subtended by the chords AC and DE at the centre.
In a cyclic quadrilateral ABCD, if ∠A − ∠C = 60°, prove that the smaller of two is 60°
In the given figure, ABCD is a cyclic quadrilateral. Find the value of x.
Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.
ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that EB = EC.
In the given figure, ABCD is a quadrilateral inscribed in a circle with centre O. CD is produced to E such that ∠AED = 95° and ∠OBA = 30°. Find ∠OAC.
ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.
