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Question
On circles O is the centre of the circle .in the given figure OA=OB=OC
Then prove that
Angle x+angle y=2(angle z+angle t)
On circles
O is the centre of the circle .in the given figure OA=OB=OCThen prove that
Angle x+angle y=2(angle z+angle t)
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Solution
O is the centre of the circle in the given Figure ij OA =OB =OC The P.T.
∠x+∠y=2(∠z+∠t)
x + y = angle subtended by chord AC at centre.
angle ABO = 90 - Z
angle CBO = 90 - T
angle ABO + angle CBO = 180 - (Z + T)
angle ABC = 180 - ( Z + T)
BUT angle ABC is angle in opposite segment of AC.= 12 Reflex (x + y)
180 - (z +T) = 12 (360 -(x +y)= 180 - (x+y)2
z+t=(x+y)2
2(z + t) = (x + y) ---proved
∠x+∠y=2(∠z+∠t)
x + y = angle subtended by chord AC at centre.
angle ABO = 90 - Z
angle CBO = 90 - T
angle ABO + angle CBO = 180 - (Z + T)
angle ABC = 180 - ( Z + T)
BUT angle ABC is angle in opposite segment of AC.= 12 Reflex (x + y)
180 - (z +T) = 12 (360 -(x +y)= 180 - (x+y)2
z+t=(x+y)2
2(z + t) = (x + y) ---proved
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