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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.

How can a quadrilateral be inscribed in a circle? – Answers – A quadrilateral is inscribed in a circle it means all the vertices of quadrilateral are touching the circle. therefore it is a cyclic quadrilateral and sum of the opposite angles in cyclic quadrilateral is supplementary. suppose if one angle is A then another will be 180 degree – angle A.Quadrilateral inscribed in a Circle. Thread starter GreenDay14. Start date Feb 16, 2010. A quadrilateral is inscribed in a circle. Prove that the sum of either pair of opposite angles equals two right angles.A quadrilateral inscribed in a circle (also called cyclic quadrilateral) is a quadrilateral with four vertices on the circumference of a circle. One example from the previous article shows how an inscribed triangle inside a circle makes two chords and follows certain theorems.

Quadrilateral inscribed in a Circle | Math Help Forum – Cyclic quadrilaterals are also called inscribed quadrilaterals or chordal quadrilaterals. A quadrilateral is cyclic when its four vertices lie on a circle. Opposite angles in a cyclic quadrilateral adds up to 180˚.Circle Inscribed in a Quadrilateral. A tangential quadrilateral is a quadrilateral whose four sides are all tangent to a circle inscribed within it. In such a quadrilateral, the sum of lengths of the two opposite sides of the quadrilateral is equal.Also, parallelograms PQRS, BPSC, and APSD are between the same parallels. Class 9 RD Sharma Solutions Chapter 14 Quadrilaterals Ex 14.2. Question 5. PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then find or(∆RAS).

Quadrilaterals in a Circle – Explanation & Examples – Transcribed Image Text from this Question. 5. (09.02 MC) A quadrilateral PQRS is inscribed in a circle, as shown below: What is the measure of arc PQR? (1 point) C 265° ? 275° 340° 190°.Answer: Option A is correct. The measure of Arc PQR is 190 degree. Step-by-step explanation: Given a cyclic quadrilateral PQRS is inscribed in a circle as First find the ; A quadrilateral is cyclic if and only if opposite angles sum to 180°. then; Substitute the value of in above equation we get; SimplifyPresentation 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.