In the given figure points A- D - P- C and B lie on a circle with centre O- BOD - 150- Find the measures of - BPD- - BCD and - BAD

2∠ BAD=∠ BOD (Property) ⇒∠ BAD=75 #176; ∠ BPD=180 #176; ∠ BAD (Opposite angle add to 180 #176; in cyclic quadrilateral) ⇒∠ BPD=105 ...

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Standard X

Mathematics

Chord Properties of Circles

In the given ...

Question

In the given figure points $A, D, P, C$ and $B$ lie on a circle with centre $O, ∠ B O D = 150^{\circ}$ Find the measures of $∠ B P D, ∠ B C D$ and $∠ B A D$

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Solution

$2 ∠ B A D = ∠ B O D$
(Property)
$\Rightarrow ∠ B A D = 75 ° ∠ B P D = 180 ° - ∠ B A D$
(Opposite angle add to $180 °$ in cyclic quadrilateral)
$\Rightarrow ∠ B P D = 105 ° ∠ B C D = 105 °$ (Sim)

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In the given figure points A,D,P,C and B lie on a circle with centre O,∠BOD=150∘ Find the measures of∠BPD,∠BCD and ∠BAD

2∠BAD=∠BOD(Property)⇒∠BAD=75°∠BPD=180°−∠BAD(Opposite angle add to 180° in cyclic quadrilateral)⇒∠BPD=105°∠BCD=105°(Sim)

In the given figure points $A, D, P, C$ and $B$ lie on a circle with centre $O, ∠ B O D = 150^{\circ}$ Find the measures of $∠ B P D, ∠ B C D$ and $∠ B A D$

$2 ∠ B A D = ∠ B O D$
(Property)
$\Rightarrow ∠ B A D = 75 ° ∠ B P D = 180 ° - ∠ B A D$
(Opposite angle add to $180 °$ in cyclic quadrilateral)
$\Rightarrow ∠ B P D = 105 ° ∠ B C D = 105 °$ (Sim)