Question

In which of the following cases is it not possible to construct a cyclic quadrilateral?

• A. Given $2$ sides and $2$ angles.
• B. Given $1$ side and $1$ diagonal.
• C. Given $1$ side and $3$ angles.
• D. Given $2$ sides and $2$ diagonals.

Answer 1

The correct option is B Given $1$ side and $1$ diagonal.

(A) Draw a line segment which forms one side of a quadrilateral.

From one end of the line, make an angle of given measure and draw an arc of given length of side.

Join the point of intersection of angle and arc and get the another side.

From one end, make an angle of given measure and draw the line. To form a quadrilateral.

(C) Draw a side of given length.

As $3$ angles are given, so we can find out the measure of $4^{th}$ angle. And then we can draw a quadrilateral.

(D) Draw one side of quadrilateral of given length.

From one of the end of side, make an arc of length of diagonal and another arc of length of given side.

Join the point of intersection from both the ends, so that they form a triangle.

Make another arc from other end of side of length of diagonal and join the ends of side with the arc to form a Quadrilateral.

But in (B), We can draw one of the side of quadrilateral and one diagonal which can't be converted into quadrilateral.

Hence, option B is correct.