Question

prove- if the digonals of the cyclic quadrilateral are perpendicular to each other show that the line passing through the point of intersection of digonals and midpoint of a side is perpendicular to the opposit side






Give quick ans plz guyz​

Answer 1

Answer:

A cyclic quadliateral ABCD in which diagonal AB and CD intersect each other cut point O . Also ,AP=BP ApO=Bpo=90

To prove CD

proof:InAPO and BPO

APO=BPO=90

AP=BP Given

side po is common

APO=BPO by (SAS)

AOP=BOP=(CPCT)

2×AOP=90

AOP=90÷2=45

IN APO

OAP+APO+POA=180 by angle sum property of triangle

OAP+90+45=180

AOP=COQ=45 BY varcticaly opposite angle

BOP=DOQ=45 " " " "

Also,angle in the same segment of a circle are equal.

BDC=CAB=45

ABD=ACD=45

Now,in OQD and OQC

45+OCQD+45=180 by angle some property of triangle

OQD= 180_90=90

Similarly==OQC=90

So, we can conclude that PQ and CD