Question

prove that the angle of major segment in an acute angle​

Answer 1

Answer:

Step-by-step explanation:

To prove : angle ACB is acute and angle ADB is obtuse. ... we know that angle subtended by an arc of a circle at its centre is twice the angle subtended by it at any point of the alternate segment of circle. Since AB is minor arc and angle ACB is the angle formed by it in alternate segment.

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.