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Chord Properties of Circles

In the given ...

Question

In the given figure, AB and AC are equal chords of a circle with centre O and $O P ⊥ A B, O Q ⊥ A C$ .
The relation between $P B$ & $Q C$ is

P B > Q C

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P B = Q C

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P B < Q C

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P B = 2 Q C

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Solution

The correct option is B $P B = Q C$
$G i v e n - A B & A C a r e e q u a l c h o r d s o f a c i r c l e w i t h c e n t r e O . O P ⊥ A B & O Q ⊥ A C . T o f i n d o u t - t h e r e l a t i o n b e t w e e n P B & Q C = ? S o l u t i o n - O P ⊥ A B & O Q ⊥ A C . ∴ O P & O Q a r e t h e d i s t a n c e s o f A B & A C f r o m O . ∵ A B = A C ⟹ O P = O Q (E q u a l c h o r d s o f a c i r c l e a r e a t e q u a l d i s t a n c e s f r o m t h e c e n t r e) . . . . . . . (i) A l s o ∠ O P B = 90^{o} = ∠ O Q C . . . . . . (i i) a n d O B = O C (r a d i i o f t h e s a m e c i r c l e) . . . . . . (i i i) . ∴ F r o m (i), (i i) & (i i i) w e c o n c l u d e t h a t Δ O P B & Δ O Q C a r e c o n g r u e n t . ∴ P B = Q C . A n s - O p t i o n B .$

Suggest Corrections

Similar questions

O

A B

A C

A B = A C

O P ⊥ A B, O Q ⊥ A C

P B = Q C

∠ P B A = 30^{\circ}

Δ

∠ A

⊥

⊥

A B \times A Q = A C \times A P

Δ

∠

⊥

⊥

B C^{2} = (A C \times C P + A B \times B Q)

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