Prove that if chords of congruent circles subtended equal angle at their centres then the chords are equal​

Step-by-step explanation:

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Let us consider two congruent circles (circles of same radius) with centres as O and O'.

In ∆AOB and ∆CO'D,

∠AOB = ∠CO'D (Given)

OA = OF (Radii of congruent circles)

OB = OD (Radii of congruent circles)

∆AOB = ∆CO'D (SAS congruence rule)

AB = CD (By CPCT)

Hence, if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

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answer:

संकेत बिंदु-(i) भूमिका (ii) मानव के लिए महत्त्व (iii) पेड़ और पर्यावरण संतुलन (iv) पेड़ और ताप नियंत्रण (५) पेड़

और जीवों का संरक्षण (vi) वृक्षारोपण अति आवश्यक (vii) उपसंहार/निष्कर्ष

answer:

Given: Teo congruent circle C

1

& C

2

equal angle at centres.

Prove: Chords are equal

Proof

Let radius of these two circles are R

Now in ΔABC and ΔPQR

∠ABC=∠PQR (given)

AB=PQ (Radius of congruent circles are equal)

BC=QR

ΔABC≅ΔPQR (SAS congruence rule)

∴AC=PR

answer:

In △AOB and △PXQ

AO=PX [Radius of congruent circles are equal]

∠AOB=∠PXQ [Given]

BO=QX [Radius of congruent circles are equal]

△AOB≅△PXQ [SAS congruence rule]

∴AB=PQ [CPCT]

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