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प्रश्न
Prove that angles inscribed in the same arc are congruent.
Given: In a circle with center C, ∠PQR and ∠PSR are inscribed in same arc PQR. Arc PTR is intercepted by the angles.
To prove: ∠PQR ≅ ∠PSR.
Proof:
`m∠PQR = 1/2 xx [m(arc PTR)]` ...(i) `square`
m∠`square` = `1/2 xx [m(arc PTR)]` ...(ii) `square`
m∠`square` = m∠PSR ...[By (i) and (ii)]
∴ ∠PQR ≅ ∠PSR
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उत्तर
Given: In a circle with center C, ∠PQR and ∠PSR are inscribed in same arc PQR. Arc PTR is intercepted by the angles.
To prove: ∠PQR ≅ ∠PSR.
Proof:
`m∠PQR = 1/2 xx [m(arc PTR)]` ...(i) \[\boxed{\text{Inscribed angle theorem}}\]
m∠\[\boxed{PSR}\] = `1/2 xx [m(arc PTR)]` ...(ii) \[\boxed{\text{Inscribed angle theorem}}\]
m∠\[\boxed{\text{PQR}}\] = m∠PSR ...[By (i) and (ii)]
∴ ∠PQR ≅ ∠PSR
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