Math, asked by Anonymous, 10 months ago

❣❣⏩⏩HELP MEE⏪⏪❣❣


23. Two circles having their centres at O and P intersect each
other at Q and R. Two straight lines AQB and CRD are
drawn parallel to OP. Prove that
(a) AB = 20P, and
(b) AB =CD.​

Attachments:

Answers

Answered by Anonymous
115

Solution :-

Provided

• AB || OP || CD

(a) To prove 2 OP = AB

Const:-

• OM and PN perpendicular to AB.

• Join QR and Mark point S where it intersect OP.

Proof :-

AQ is a chord , hence the perpendicular from center will bisect it.

→ 2 OS = AQ ...(i)

QB is a chord , hence the perpendicular from center will bisect it.

→2 SP = QB ....(ii)

Add (i) & (ii)

→ 2 ( OS + SP ) = AQ + QB

→ 2 OP = AB

(b) To prove AB = CD

Const:-

• Join QR and Mark point S where it intersect OP.

• Join OQ , OR , PR & PQ

Here

• QS = height of ∆OPQ

• RS = height of ∆OPR

Now in ∆OPQ & ∆OPR

• OP = OP ( common)

• OQ = OR ( raddii)

• PQ = PR (raddii)

Hence ∆OPQ ≅ ∆OPR

Therefore , SQ = SR ( cpct)

Now distance of

• Chord AQ from Center = Chord CR from center

→ AQ = CR ( property of circle that Chords equidistant from center have same length) ...(i)

• Chord QB from Center = Chord RD from center

→ QB = RD ( property of circle that Chords equidistant from center have same length) ...(ii)

Add (i) & (ii)

→ AQ + QB = CR + RD

→ AB = CD

Attachments:

Anonymous: congrats on completing 1k answers! ❤️
Anonymous: Thanks Bhavna ^^
Answered by brainlybunny
2

Step-by-step explanation:

Hope it helps!!!!!!!!!

Attachments:
Similar questions