Question

In a quadrilateral ABCD with AB = AD = 6cm, $\angle A=45°$ BC = 3.5cm, CD = 5cm ,can we construct a point which is equidistant from BC and CD?

• A. Yes.
• B. Never possible.
• C. Equidistant point cannot be found.
• D. Data insufficient.

Answer 1

The correct option is A Yes.

Steps of construction:

1. Draw a line segment AB of length 6cm.

2. Construct an angle of 45° at the point A. Keeping A as the centre, cut an arc of radius 6cm and mark the point to be D.

3. Now, keeping B and D as the centers cut two arcs of radius 3.5cm and 5 cm respectively.

4. Mark the intersecting point to be C and join C to B and D.

5. Construct an angle bisector for the $\angle BCD$ and extend the line.

6. The angle bisector and the line BD intersect at a point. Mark that point to be P.

This point P is equidistant from BC and CD.
Hence, we can construct a point with the given information.