Question

please answer question in image

Answer 1

Step-by-step explanation:

Figure PORC is a square (all angles 90 degree and 2 adjacent sides are equal).

Let the radius be r.

Then,

PC=OP=OR=RC=r

PC=r

== AP = b-r

CR=r

== BR=a-r

Now,

From point A to the inscribed circle,

AP=AQ = b-r

BR=BQ = a-r

(Since tangents from an exterior point to a circle are equal)

also,

AQ+BQ= AC = c (given)

so,

b-r+a-r=c

== b+a-2r=c

== a+b-2r=c

== a+b-c=2r (Transposing c and 2r)

Hence Proved.                                                                                        Q.E.D