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## A quadrilateral PQRS is inscribed in a circle. Is PQRS a square? : Data Sufficiency (DS)

amanvermagmat wrote:

A quadrilateral PQRS is inscribed in a circle. Is PQRS a square?

(1) PQRS is a rhombus.

(2) Diagonals of PQRS are equal.

Statement 1 alone is sufficient to state that PQRS is a square.

A rhombus consists of all equal sides and its diagonals are perpendicular bisectors. Considering, the quadrilateral PQRS is inscribed inside the circle, all the points of PQRS must lie on the circle.

If all points like on the circle and the sides are to be equal then the diagonals of the rhombus are diameters of the circle. And we know that any triangle formed with one of the sides as the diameter will have the angle opposite to the side to be 90.

Hence, all angles are 90 and all sides are equal.

The answer should be A.

Quadrilateral OPQR is inscribed inside a circle as shown below. – is the measure of angle O? You must show all work and calculations to receive credit. If random variables, A, B, C are tangent points of the circle inscribed in a triangle /ABC wit its sides.Presentation on theme: "Geometry Mini-Lesson Gabriel inscribed quadrilateral ABCD in a circle, as shown below. Arcs AB and BC both measure 85° and arcs CD and DA both The pizza was delivered in a square box with length 18 inches. The pizza fit perfectly in the box, as shown in the image below.GIVEN: ABCD is a cyclic quadrilateral. As it is inscribed in a circle. Related Questions. More Answers Below. Originally Answered: ABCD is a quadrilateral inscribed in a circle with AB=2, BC=√6−√2, ∠BAD=75∘ and ∠ABC=135∘. What is the value of CD^2?

Geometry Mini-Lesson Gabriel inscribed quadrilateral ABCD in… – Here you'll learn properties of inscribed quadrilaterals in circles and how to apply them. This video gives more detail about the mathematical principles presented in Inscribed Quadrilaterals in Grade10 LT5: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.Definition and properties of a quadrilateral inscribed in a circle. In the figure above, as you drag any of the vertices around the circle the quadrilateral will change. As with all polygons, this is not regarded as a valid quadrilateral, and most theorems and properties described below do not hold for…Circle O is shown with a quadrilateral ABCD inscribed inside it. Angle A is labeled x plus 16. Quadrilateral ABCD is inscribed in a circle. Find the length of its shorter diagonal if AB=12, CD=18, arc BC=120, and arc AD =60°.

The quadrilateral ABCD is inscribed in a circle .The… – Quora – since the quadrilateral is inscribed in a circle.. sosum of opposite sides will be equal. i.e 4RS=2QR A/Q, perimeter of square equals to perimeter of qudrilateral =>4RS+2QR=24 =>RS=3 AND QR=6 NOW, by drawing SM ll QR, and SD as height of triangle SMP we get euilateral triangle SMP.Hide Show timer Statistics. A quadrilateral PQRS is inscribed in a circle. A rhombus consists of all equal sides and its diagonals are perpendicular bisectors. Considering, the quadrilateral PQRS is inscribed inside the circle, all the points of PQRS must lie on the circle.PQRS is an isosceles trapezium. if PQRS is inscribed in a circle and PS = QR, Step-by-step explanation pq and rs are two equal chords of a circle with centre Such that brainly.in/question/13185715. recall that two circles are congruent if they have the same radii prove