Question

C
1.
Р
In the following figure, AOB is a straight angle. OQ
is the bisector of AOC and OP is the bisector of BOC.
B
O
If AOC = 60°, then find i) BOC ii) POQ.​

Answer 1

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In figure 11, OP bisects ∠AOC, OQ bisects ∠BOC and OP⊥OQ. Show that the points A,O and B are collinear.

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ANSWER

Given:

OP bisects ∠AOC, OQ bisects ∠BOC and OP⊥OQ

To prove: The points A,O and B are collinear.

Proof:

Since, OP bisects ∠AOC,

∠AOP=∠COP …… (1)

Since, OQ bisects ∠BOC,

∠BOQ=∠COQ …… (2)

Now, ∠AOB

=∠AOP+∠COP+∠COQ+∠BOQ

=∠COP+∠COP+∠COQ+∠COQ

From (1) and (2), we have

=2(∠COP+∠COQ)

=2∠POQ

=2(90

∘

)

=180

∘

Therefore, points A,O and B are collinear.