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
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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
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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