Question

Use a ruler and compass to answer this question.

1. Construct a circle of radius 4.5 cm and draw a chord AB of length 6.5 cm. 
2. At A, construct ∠CAB = 75°, where C lies on the circumference of the circle. 
3. Construct the locus of all points equidistant from A and B. 
4. Construct the locus of all points equidistant from CA and BA. 
5. Mark the point of intersection of the two loci as P. Measure and write down the length of CP.

Answer 1

Steps of construction:

1. With O as the center, draw a circle of radius 4.5 cm.
2. Take a point A on the circumference; with A as the center, cut an arc of radius 6.5 cm, intersecting the circumference at point B.
3. Construct ∠CAB = 75°, where C lies on the circumference of the circle.
4. Draw XY, the perpendicular bisector of AB.
5. Draw AZ, the angular bisector of angle A.
6. Mark point P as the intersection of AZ and XY.
7. Measure CP.

Hence, the length of CP is 5.2 cm.