Bissoy.com
Doctors Medicines MCQs Q&A

Which of the following statements is/are true? A: In a cyclic quadrilateral ABCD, If two diagonals AC and BD intersect each other at O, then OA × OB = OC × OD. B: In a quadrilateral (kite), the smaller diagonal divides the kite into two equilateral triangles. C: Diagonals of a rectangle are diameter of its circumcircle. 

Which of the following statements is/are true? A: In a cyclic quadrilateral ABCD, If two diagonals AC and BD intersect each other at O, then OA × OB = OC × OD. B: In a quadrilateral (kite), the smaller diagonal divides the kite into two equilateral triangles. C: Diagonals of a rectangle are diameter of its circumcircle.  Correct Answer Only C

CONCEPT:

Properties of quadrilaterals like square, rectangle, rhombus, trapezium, kite and cyclic quadrilateral.

FORMULA USED:

When two chords AC and BD of a circle intersect each other at O, then :

OA × OC = OB × OD 

CALCULATION:

A:

[ alt="F1 A.K 15.6.20 Pallavi D16" src="//storage.googleapis.com/tb-img/production/20/06/F1_A.K_15.6.20_Pallavi_D16.png" style="width: 161px; height: 173px;">

The two diagonals of a cyclic quadrilateral are also the chords of circle. When two chords AC and BD intersect each other at O, then OA × OC = OB × OD.

B: In a quadrilateral (kite), the smaller diagonal divides the kite into two isosceles triangles.

C: When a circumcircle of a rectangle is drawn, then a diagonal of the rectangle is always the diameter of its circumcircle.

Hence, only C is true.

Related Questions

Given steps in procedure to find the center of gravity of the quadrilateral ABCD. Arrange the steps. i. Draw lines joining G1 with G2 and G3 with G4. ii. In given quadrilateral draw diagonal BD and locate centers of gravity G1, G2 of triangles BCD and ABD. iii. The point of intersection of lines G1G2 and G3G4 gives the center of gravity of the quadrilateral ABCD. iv. Similarly draw the diagonal AC and determine the centers of gravity G3, G4 of triangles ABC and ADC.
Which of the following statements is/are true? A: The ratio between the radius of circumcircle and that of incircle of a square is √2 : 1. B: A diagonal of a rectangle divides it into two equal isosceles triangles. C: In a trapezium ABCD, AB and CD are parallel to each other, then ∠BAD + ∠CDA = 180°.
Suppose chords AB and CD of a circle intersect at a point P inside the circle. Two right-angled triangles A’P’B’ and C’Q’D’ are formed as shown in the figure below such that A’P’ = AP, B’P’ = BP, C’Q’ = CP, D’Q’ = DP and ∠A’P’B’ = 90° = ∠C’Q’D’. Which of the following statements are not correct? 1. A’P’B’ and C’Q’D’ are similar triangles, but need not be congruent 2. A’P’B’ and C’Q’D’ are congruent triangles. 3. A’P’B’ and C’Q’D’ are triangles of same area. 4. A’P’B’ and C’Q’D’ are triangles of same perimeter. Select the correct answer using the code given below.
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image
Select three out of five combination of the parts 1, 2, 3, 4 and 5 which can fit into each other to form an equilateral triangle.
Construction of Squares and Triangles mcq question image