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)

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

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