Question 28
Let $ABC$ be a right triangle with $\angle ABC = 90^\circ$. Points $P, Q, R$ lie on the sides $BC, CA, AB$, respectively, in such a way that conditions
$$
AQ : QC = 2 : 1, \quad AR = AQ, \quad QP = QR, \quad \angle PQR = 90^\circ
$$
are satisfied. Find the value of $AR$ if $CP = 1$. Here for a line segment $XY$ its length is also represented by $XY$.
$$
AQ : QC = 2 : 1, \quad AR = AQ, \quad QP = QR, \quad \angle PQR = 90^\circ
$$
are satisfied. Find the value of $AR$ if $CP = 1$. Here for a line segment $XY$ its length is also represented by $XY$.