Question

Four roads have to be constructed by touching village Khanpur in circular shape
of radius 1700 m in the following manner as shown in attached image.

Savita got contract to construct the roads AB and CD while Vijay got contract to
construct AD and BC.

Prove that AB + CD = AD + BC.

Which value is depicted by the contractor?

Answer 1

we need to construct points E B/W AB ,
F B/W BC, G B/W DC, H B/W AD

T/P AB+CD=AD+BC
AE=AH. [ tangents meeting outside the circle at
BE=BF. a point are always equal or through
DG=DH. theorum]
CG=CF
[AB+BE]+[DG+CG]=AH+BF+DH+CF
AB. +. CD. =[AH+DH]+[BF+CF]
AB. +. CD. = AD. +. BC

Answer 2

SOLUTION :-

here,

AP = AS...( 1 ) } tangents

BP= BQ.....( 2 ) } from

CR = CQ.....( 3 ) } same

DR = DS.......( 4 ) } external

point

Now, adding Equation ( 1 ), ( 2 ), ( 3 ), and ( 4 )
we get,

AP + BP +CR + DR = AS + BQ + CQ+ DS

AP + CD = AD + BC .hence, proved.

The values are as follows :-

All the sides of the village are connected to roadways
which shows intelligence, in planning of the roadways