Q. 14.3( 12 Votes )

# In Fig. 16.120, *O* is the centre of the circle. If ∠*APB*=50°, find ∠*AOB* and ∠*OAB*.

Answer :

∠APB = 50^{o} (Given)

By degree measure theorem,

∠AOB = ∠APB

∠APB = 2 * 50

= 100^{o}

Since,

OA = OB (Radii)

Hence,

∠OAB = ∠OBA (Angle opposite to equal sides are equal)

Let,

∠OAB = x

In Triangle OAB,

∠OAB + ∠OBA + ∠AOB = 180^{o}

x + x + 100^{o} = 180^{o}

2x = 80^{o}

x = 40^{o}

∠OAB = ∠OBA = 40^{o}

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PREVIOUSA circular park of radius 40 m is situated in a colony. Three boys Ankur, Amit and Anand are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.NEXTIn Fig. 16.121, it is given that O is the centre of the circle and ∠AOC=150°. Find ∠ABC.

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In the given figure, O is the centre of a circle and ∠BCO = 30°. Find x and y.

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