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We will be happy to post videos as per your requirements also. Do write to us.The following are circle theorems on arc and angle.
|1) ∠POM = ∠OPM + ∠ORP||1) By exterior angle theorem (∠POM is exterior angle)|
|2) OP = OR||2) Radii of same circle|
|3) ∠OPR = ∠ORP||3) In a Δ two sides are equal then the angle opposite to them are also equal.|
|4) ∠POM = ∠ORP + ∠ORP||4) Substitution property. From (1)|
|5) ∠POM = 2∠ORP||5) Addition property.|
|1) ∠POM = ∠OPR + ∠ORP||1) Exterior angle theorem.|
|2) ∠POM = ∠ORP + ∠ORP||2) As,OP = OR = radius. ∴∠ORQ = ∠ORP|
|3) ∠POM = 2∠ORP||3) Substitution and addition property.|
|4) ∠QOM = ∠ORQ + ∠OQR||4) Exterior angle theorem.|
|5) ∠QOM = ∠ORQ + ∠ORQ||5) As, OQ =OR = radius, ∴ ∠ORQ = ∠OQR|
|6) ∠QOM = 2∠ORQ||6) Substitution and addition property.|
|1) ∠POM = ∠OPR + ∠ ORP||1) By exterior angle theorem.|
|2) ∠POM = 2∠ORP||2) As, OP = OR = radius, ∴∠OPR = ∠ORP and by addition property|
|3) ∠ QOM = ∠ORQ + ∠OQR||3) By exterior angle theorem in ΔQOR|
|4) ∠QOM = 2∠ORQ||4) As, OP = OR = radius, ∴∠ORQ = ∠OQR and by addition property|
|5) ∠POM + ∠QOM = 2(∠ORP + ∠ORQ)||5) From (2) and (4)|
|6) Reflex ∠POQ = 2∠PRQ||6) Reflex of ∠POQ =∠POM + ∠QOM|
|1) ∠POQ = 2∠PRQ||1) Angle subtended by an arc of a circle at its center is twice the angle formed by the same arc.|
|2) 180 0 = 2∠PRQ||2) As POQ is a straight line|
|3) ∴ ∠PRQ = 90 0||3) Division property|
Russia-Ukraine crisis update - 3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.