Chapter 10.8, Problem 19WE

To determine

Draw an angle an three segments r , s , and t as shown.Construct AB so that AB = t .Then construct the locus of points P such that $m\angle APB=n$ .

Answer to Problem 19WE

Locus is circle

Explanation of Solution

Given:

  

Calculation:

Construct the segment and angle :

  

Now construct AB so that AB = t .

  

OM is perpendicular bisector of AB, since the centre of the locus circle will lie on the perpendicular bisector of AB.

By inscribed angle theorem , all the angles subtended by an arc of a circle on circumference is half of the angle subtended on the center.

The locus of all the points P such that $m\angle APB=n$ is circle with AB as a chord that subtends $\angle APB=n°$ on the circle and $\angle AOB=2n°$ , where O is the center of the circle.