Kindly solve these 2 questions?

(a)

O is the center of in-circle of the right angled triangle #ABC# in which #/_ABC=90^@#

O being the in-center of the #DeltaABC#

#DeltaAODcongAOF#

So #AD=AF#

#OD=OF=r("radius of incircle")#

#DeltaCOEcongCOF#

So #CE=CF#

#OE=OF=r("radius")#

#DeltaBODcongBOE#

So #BD=BE#

#OD=OF=r("radius")#

Again #/_DBE=/_ABC=90^@#

Hence #BDOE" is a square"#

Now

#AB+BC-AC#
#=(BD+AD)+(BE+CE)-(AF+FC)#

#=(BD+BE)+AD-AF+CE-CF#

#=(r+r)+AD-AD+CE-CE#

#=2r="Diameter of the incircle"#

(b)

By sine law we have for #DeltaABC#

#a/sinA=b/sinB=c/sinC=2R.......[1]#,

where R is the radius of the circumcircle of #DeltaABC#

Now from relation [1] we have

#b=2RsinB#

#=>bc=2RcsinB#

#=>bc=2Rcxxh/c#,

where h is the length of the perpendicular from A to BC

So

#=>bc=2Rxxh#

#="diameter" xx" length of the perpendicular from A to BC"#

This relation can be proved similarly for any pair of sides of #DeltaABC#

So for a triangle inscribed in a circle, the product of any two sides of the triangle is equal to the product of the diameter and the perpendicular distance of the third side from the opposite vertex