Two chords AB and CD of circle whose centre is O- meet the point P and angle AOC-50-o- angle BOD-40-o- Then the value of angle BPD is-60-o-40-o-75-o-45-o-

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Toppr Admin · Accepted Answer

-x2220-AOC-BOD-2-x2220-ABC-2-x2220-BCD-2-x2220-ABC-x2220-BCD-2-x2220-BPD- since- angle formed on major arc is half of the angle formed on center-x2234-x2220-AOC-x2220-BOD-2-x2220-BPD2-x2220-BPD-50o-40o-x2220-BPD-90o2-45o

Two chords $A B$ and $C D$ of circle whose centre is $O$ , meet at the point $P$ and $∠ A O C = 50^{o}, ∠ B O D = 40^{o}$ . Then the value of $∠ B P D$ is:
$60^{o}$
$40^{o}$
$75^{o}$
$45^{o}$

$∠ A O C + B O D = 2 ∠ A B C + 2 ∠ B C D$
$= 2 ∠ A B C + ∠ B C D$
$= 2 ∠ B P D$ ......
( since, angle formed on major arc is half of the angle formed on center)
$∴ ∠ A O C + ∠ B O D = 2 ∠ B P D$
$2 ∠ B P D = 50^{o} + 40^{o}$
$∠ B P D = \frac{90^{o}}{2} = 45^{o}$

Two chords AB and CD of circle whose centre is O, meet at the point P and ∠AOC=50o,∠BOD=40o. Then the value of ∠BPD is:60o40o75o45o

∠AOC+BOD=2∠ABC+2∠BCD=2∠ABC+∠BCD=2∠BPD......( since, angle formed on major arc is half of the angle formed on center)∴∠AOC+∠BOD=2∠BPD2∠BPD=50o+40o∠BPD=90o2=45o

Two chords $A B$ and $C D$ of circle whose centre is $O$ , meet at the point $P$ and $∠ A O C = 50^{o}, ∠ B O D = 40^{o}$ . Then the value of $∠ B P D$ is:
$60^{o}$
$40^{o}$
$75^{o}$
$45^{o}$

$∠ A O C + B O D = 2 ∠ A B C + 2 ∠ B C D$
$= 2 ∠ A B C + ∠ B C D$
$= 2 ∠ B P D$ ......
( since, angle formed on major arc is half of the angle formed on center)
$∴ ∠ A O C + ∠ B O D = 2 ∠ B P D$
$2 ∠ B P D = 50^{o} + 40^{o}$
$∠ B P D = \frac{90^{o}}{2} = 45^{o}$