Question

M point is on Chord AB such that PA = PM. Show that BM = BQ
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Please help quickly

Answer 1

Answer:

Proved in the attached file

Step-by-step explanation:

Q: M point is on Chord AB such that PA = PM. Show that BM = BQ

Answer 2

Process 1.

According the question :-

1. AB and PA       ( given)

2. PA = PM          ( given)

We have to prove that :-

BM = BQ

Let,s join point P and point Q . Now PQ and AB are two chords who are intersected at the point M.

• Chord PQ and Chord AB bisects at point M.
• AB bisects PQ , hence PM =QM          
• PQ bisects AB, hence , AM= BM,        

∴ PM ×MQ = AM ×BM  ..    (1)   ( internal division of chords theorem)

  AM × MQ = AM ×BM              

( as we know  PM = AM)

Hence MQ = BM

Therefore it is proved that :-

BM = BQ

Ans:- BM = BQ

#SPJ3

Process 2.

According the sum, Δ PAM and ΔBQM both are formed on the same chord AB.

therefore:-

• ∠BAP = ∠BQP     ..( both angles lied on same chord )
• ∠PMA =∠BMQ   .. ( opposit angles are equal)
• ∴ Δ PAM ≅ ΔBQM

Hence :-

$\frac{PA}{BQ}$ = $\frac{PM}{BM}$

⇒  $\frac{PA}{BQ}$ = $\frac{PA}{BM}$

⇒ BQ = BM

Hence proved.

Ans :- BQ = BM

#SPJ3