Question

in the given figure if o is the centre of the circle in the determine APB​

Answer 1

Step-by-step explanation:

APB = 50° (Given) By degree measure theorem: ∠AOB = 2∠APB ∠AOB = 2 × 50° = 100° Again, OA = OB [Radius of circle] Then ∠OAB = ∠OBA [Angles opposite to equal sides] Let ∠OAB = m In ΔOAB, By angle sum property: ∠OAB +∠OBA + ∠AOB = 180° => m + m + 100° = 180° => 2m = 180° – 100° = 80° => m = 80°/2 = 40° ∠OAB = ∠OBA = 40°Read more on Sarthaks.com - https://www.sarthaks.com/612456/in-figure-o-is-the-centre-of-the-circle-if-apb-50-find-aob-and-oab

Answer 2

Step-by-step explanation:

∠ADC=

2

1

∠AOC

(Angle subtended by a chord on mayor area is half of that subtended on center)

∴∠ADC=

2

1

×130=65

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Now, ADCB is cyclic quadrilateral ⇒

Sum of opposite Angles is 180

∘

∴∠ABC+∠ADC=180

∘

∠ABC+65=180

∘

∠ABC=115

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