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its sideways and i am disabled, so turn it upside down...
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Step-by-step explanation:
Let ABCD be a quadrilateral a circle with centre 0
Now join AO,BO,CO,DO
from the figure ΔDAO = ΔBAO = 1
Also ΔABO= ΔCBO ( since, BA & BC are tangents)
Let ΔABO=ΔCBO=2
similarly we take the same way for vertices C & D
Sum of the angles at the center is 360degrees
Recall that sum of the angles in quadrilateral, ABCD=360degrees
=2(1+2+3+4)=360degrees
=1+2+3+4=180degrees
in ΔAOB, ΔBOA=180(1+2)
inΔCOD, ΔCOD=180(3+4)
ΔBOA +ΔCOD=360(1+2+3+4)=360-180 =180
since AB & CD subtend supplementary angles at 0
thus opposite sides of a quadrilateral cirumscribing a circle subtend supplementary angles at the center of the circle
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