Q25 of 100 Page 17

Prove that the angle in a segment shorter than a semicircle is greater than a right angle.

Given that,

∠ACB is an angle in minor segment


To prove: ∠ACB > 90o


Proof: By degree measure theorem


Reflex ∠AOB = 2 ∠ACB


And,


Reflex ∠AOB > 180o


Then,


2 ∠ACB > 180o


∠ACB >


∠ACB > 90o


Hence, proved


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23

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA=ED. Prove that:

(i) AD||BC (ii) EB=EC

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Prove that the angle in a segment greater than a semi-circle is less than a right angle.

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ABCD is a cyclic trapezium with AD||BC. If ∠B=70°, determine other three angles of the trapezium.