given figer , AB is a chord of a circle with center O and AB is produced to C such that BC equal to OB also, CO is joined and produced to meet the circle in D . if angle ACD equl to angle y and angle AOD is equal to , prove that x equal to 3y.
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OB = BC
∴ ∠BCO = ∠BOC = ∠y. ( angles opp. to equal sides are equal)
And, ∠ABO = ∠BCO + ∠BOC. ( exterior angle property)
∠ABO =∠y + ∠y = 2∠y
And, in ΔABO, ∠AOB = 180- (∠ABO + ∠BAO)
= 180 - (2y+2y). (Angles opp. to equal sides are equal)
= 180 - 4y
∠x = 180° - (∠AOB + ∠y). ( angles in a straight line)
∠x = 180° - (180-4y + ∠y)
∠x = 180° - (180-3y)
⇒ ∠x = 3y
Hope this helps you!
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∴ ∠BCO = ∠BOC = ∠y. ( angles opp. to equal sides are equal)
And, ∠ABO = ∠BCO + ∠BOC. ( exterior angle property)
∠ABO =∠y + ∠y = 2∠y
And, in ΔABO, ∠AOB = 180- (∠ABO + ∠BAO)
= 180 - (2y+2y). (Angles opp. to equal sides are equal)
= 180 - 4y
∠x = 180° - (∠AOB + ∠y). ( angles in a straight line)
∠x = 180° - (180-4y + ∠y)
∠x = 180° - (180-3y)
⇒ ∠x = 3y
Hope this helps you!
Please please mark brainliest answer, it would mean a lot to me!
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