in the given figure , o is centre of the circle, <ADC=110 and chord BC= chord BE . find the measure of <CBE

Here , Let the point of intersection of CE and OB be M

BC = CE. ( Given ) ...........1
angle BCE = angle BEC ( Angle opposite to equal sides are equal ). ...........2

Now , In triangle BME and triangle BCE
BC= BE (from 1 )
angle BCE = angle BEC (from 2 )
BM = MB (common )
So , by SAS congruence criterion
triangle BME congruent triangle BCE
angle CBM = angle EBM ( By CPCT ). ......3

Now , ABCD is cyclic quadrilateral
angle D + angle CBM = 180°
angle CBM = 70°
angle CBM + angle CBE = 70°+70° ( from 3 )
angle CBE = 140 °

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140°
  • -2
160°
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sorry umm calculation mistake...
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