Question

Opqr is a sqaure. A circle is drawn with centre o cuts the square in x and y. Prove that qx=qy

Answer 1

Answer:

This can be proved by proving triangles ΔXPQ and ΔYRQ congruent to each other and applying cpct .

Step-by-step explanation:

According to diagram shown in picture -

OP = OR    (sides of square are equal)                    ....................(1)

Also, OX = OY     (both are radii of circle)                ....................(2)

Subtracting equation (2) from (1)

=>  OP - OX = OR - OY

=> XP = RY                                 .......................(3)

We consider the ΔXPQ and ΔYRQ

Here,  XP = RY                (Proved above in equation (3))

         ∠XPQ = ∠YRQ  =  90°       (angles of a square)

          PQ  = RQ                       (sides of a square are equal)

Thus, ΔXPQ ≅ ΔYRQ              (By SAS Theorem)

So,  XQ = YQ                         (cpct)

Hence proved .