Quadrilateral has an inscribed circle which touches sides and at and respectively

MATHEMATICS · Subjective · ICSE · Mathematics · Geometry · Geometry

Problem

Quadrilateral

ABCD

has an inscribed circle which touches sides

AB,\,BC,\,CD

and

DA

W,\,X,\,Y

and

Z

respectively. If

AB=14\,\text{cm}

BC=11\,\text{cm}

and

CD=6\,\text{cm}

, (i) Prove that

AW=AZ

BW=BX

CX=CY

and

DY=DZ

. (ii) Using these relations, find the length of side

DA

. (iii) Determine the perimeter of quadrilateral

ABCD