Question

Keshawn is constructing the inscribed circle for △PQR. He has already used his compass and straightedge to complete the part of the construction shown in the figure.
Which construction could be his next step?

Answer 1

For a better understanding of the question please find the diagram in the file that has been attached. This diagram tells us till where Keshawn has completed here construction.

As we can see there is an intersection point of AB and CD and that point is X. That point is of utmost importance to Keshawn. Thus, Keshawn's next step will be to construct the perpendicular to QR, which is AB, that passes through point X. He will then place the point of the compass on the intersection of AB and CD and extend the compasses to point R, or to point Q, to point P, as all are equidistant.

Keshawn will then draw a circle with center at the intersection of AB and CD and the radius as any of the three distances, which will make the circle pass through the points, P, Q and R.

Answer 2

Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.