Properties of Cyclic Quadrilateral
Trending Questions
Q. 30. The sum of the pair of opposite angles of a cyclic quadrilateral is 180 degree
Q. 54. Prove that the angle bisectors of the angles formed by producing opposite sides of cyclic quadrilateral (provided they are not parallel) intersect at right angles?
Q. If two opposite sides of a cyclic quadrilateral are equal, then the other two sides are parallel
Q.
In the given figure, if ∠AOC=120∘, then ∠ABC = _______.
- 50∘
- 120∘
- 100∘
- 60∘
Q. 53 The angles of quadrilateral are in the ratio 3:5:9:13.Find all the angles of the quadrilateral
Q. ABCD is a cyclic quadrilateral. The diagonals of the quadrilateral intetsect at right angles. Prove that the perpendicular drawn from their point of intersection to one side when extended bisects he other side a
Q.
Question 4
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC⊥BD. Prove that PQRS is a rectangle.
Q. If a quadrilateral is cyclic, then sum of each pair of opposite angles is 180o.
Q. 34. prove that the perpendicular bisectors of the side of cyclic quadrilateral are conccurrent
Q. 23. In the given figure, P, Q and R are the mid-points of sides AB, AC and BC of AABC respectively If ADBC, then prove that PQRD is a cyclic quadrilateral. D R [(C)" ()" ()oz .(v)61 .suy]
Q. In a cyclic quadrilateral ABCD, ∠A=(2x+4), ∠B=(y+3), ∠C=(2y+10), ∠D=(4x−5). Find the four angles.
Q. If ABCD is a cyclic quadrilateral and ∠A=120°−x°, then ∠C=
- 60° + x°
- 90° + x°
- 60° - x°
- 90° - x°
Q. ABCD is a cyclic quadrilateral inscribed in a circle with the centre O. Then ∠OAD is equal to:
- 30∘
- 60∘
- 40∘
- 50∘
Q. Two circles intersect at P and Q. A secant passing through P intersects the circles in A and B respectively. Tangents to the circles at A and B intersect at T. Prove that A, Q, T and B are concyclic.
Q. 72. In a cyclic quadrilateral opposite sides are equal then prove that other two sides are parallel.
Q. O is the centre of the circle as shown in the figure, ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm. What is the measure of ∠ROQ in degrees?
- 70
Q. O is the centre of the circle as shown in the figure, ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm. What is the measure of ∠ROQ in degrees?
- 70
Q. O is the centre of the circle as shown in the figure, ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm. What is the measure of ∠ROQ in degrees?
- 70
Q.
If the quadrilateral formed by joining the mid-points of the adjacent sides of quadrilateral ABCD is a rectangle, show that the diagonals AC and BD intersect at right angle.
State true or false:
- True
- False
Q.
ABCD is a parallelogram with ∠ABC =90∘, then number of right angles in the parallelogram excluding ∠ABC is/are ____
Q. 47. The angles of quadrilateral are in ratio 3:5:9:13.find all the angles of the quadrilateral
Q.
PQRS is a cyclic quadrilateral ∠P=3x, ∠Q=y, ∠R=x, ∠S=5y. Find x and y.
Q. pqrs is a cyclic quadrilateral. If <P=3x, <Q=y, <R=x, <S=5y, find the measure of each of its angle
Q. Let ABCD be a parallelogram such that AB = q , AB = p, and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by
- →r=3→q−3(→p⋅→q)(→p⋅→q)→p
- →r=−→q+(→p⋅→q)(→p⋅→q)→p
- →r=−→−q+(→p⋅→q)(→p⋅→p)→p
- →r=−3→q−3(→p⋅→q)(→p⋅→q)→p
