Question

ABCD is a square with length of each side 10 cm.

P, Q, R and S are midpoints of sides AB, BC, CD and DA.

X, Y, Z and W are midpoints of sides PQ, QR, RS and SP.

A circle internally touches all sides of quadrilateral XYZW.

Find area and circumference of this circle.

Answer 1

Answer:

area=550/14 cm² and perimeter =110root2/7 cm

Step-by-step explanation:

ABCD is a square of each side measuring 10cm

diagonal AC= 10root2 cm

As we know that, in a triangle, line joining the mid points of 2 sides = half of the 3rd side,

hence, in triangle ABC, P and Q are mid points of side AB and BC.

So, PQ=1/2 of AC

PQ=10 root 2 /2= 5root2

similarly , We will get that PQ=PS=SR=QR. Hence PQRS is also a square and line segment XZ Joining the mid points of PS and QR= PQ i.e. XZ=PQ =5 root2

and XZ is the diameter of circle.

radius will be 5 root2/2.

By circle's area and circumference formula, you can have ur answer same what I have above.

*PLZZ DO MARK ME AS BRAINLIEST*

This was also a tricky question