Question

prove theorem 2 of chapter circle of class9

Answer 1

given;
circle with centre o
ab and cd are chords
<AOB=<COD
to prove chord AB=chordCD
​proof;
OA=OC (radii of the same circle)
OB=OD(radii of the same circle)
<AOB=<COD (given)
therefore triangle AOB congruent to triangle COD(SAS rule)
therefore AB=CD(CPCT )

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Answer 2

Step-by-step explanation:

THEOREM 10.2

If the angles subtended by the chords of the circle ar the center are equal, then the chords are equal.

Given :- A circle with center O.

AB and CD are chords that subtend equal angles at center i.e. angle AOB = angle DOB

To Prove :- AB = CD

Proof :- In triangle APB & triangle DOC

OA = OD ( radius)

angle AOB = angle DOC ( given)

OB = OC ( radius)

hence, triangle APB is congruent to triangle COD ( S-A-S Congruensy)

Hence, AB = CD ( CPCT)

hence, proved.