Question

prove that : a) angle in the major segment of a circle is acute b) angle in the minor segment of circle is obtuse

Answer 1

PSQ is major segment. and PRQ is minor segment in the circle.
we have to prove: angle prq is acute and   psq is obtuse.
* Draw  op, oq and pq.
We know that-- angle suspended by arc of circle at center is twice the angle suspended at any point on remaining part of the circle.
so, ∠ poq =2∠prq
but  ,  2∠ poq <180° (∵ ∠ of Δpoq)

∠poq<90°.  ----> acute angle.

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now reflex angle poq = 2∠psq
but ∠ poq >180°.
so 2∠psq >180°
     ∴∠psq>90°  ---->obtuse angle.
 

Answer 2

Answer:

Step-by-step explanation:

PSQ is major segment. and PRQ is minor segment in the circle.

we have to prove: angle prq is acute and   psq is obtuse.

* Draw  op, oq and pq.

We know that-- angle suspended by arc of circle at center is twice the angle suspended at any point on remaining part of the circle.

so, ∠ poq =2∠prq

but  ,  2∠ poq <180° (∵ ∠ of Δpoq)

∠poq<90°.  ----> acute angle.

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now reflex angle poq = 2∠psq

but ∠ poq >180°.

so 2∠psq >180°

     ∴∠psq>90°  ---->obtuse angle.