Question

Use ruler and compass for this question. Construct a circle of radius 4.5 cm. Draw a chord AB = 6 cm.

1. Find the locus of points equidistant from A and B. Mark the point where it meets the circle as D. 
2. Join AD and find the locus of points which are equidistant from AD and AB. Mark the point where it meets the circle as C.
3. Join BC and CD. Measure and write down the length of side CD of the quadrilateral ABCD.

Answer 1

With centre O, draw a circle of radius 4.5 cm.

On the circle, mark a chord AB = 6 cm.

1. Locus of points equidistant from A and B
   • 3. Construct the perpendicular bisector of AB.
   • This line is the locus of all points equidistant from A and B.
   • 4. Let it cut the circle at the lower point D.
2. Locus of points equidistant from AD and AB
   • Join A to D.
   • At A, construct the angle bisector of ∠DAB.
     This line is the locus of all points equidistant from lines AD and AB.
   • Let it meet the circle (on the side of B) at C.
3. Measure CD 
   • Join BC and CD to form quadrilateral ABCD.
   • Measure CD with a ruler.

CD ≈ 1.8 cm (and BC ≈ 1.5 cm).