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MathsGee Android Q&A

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In the diagram below, BOC is a diameter of the circle. AP is a tangent to the circle at A and AE=EC.

 

Prove that:

  1. BA $\parallel$ OD
  2. AOCD is a cyclic quadrilateral
  3. DC is atangent to the circle at C

 

 

in Mathematics by Platinum (147,718 points) | 1,265 views

1 Answer

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1. BAC= 90, <s in a semi circle

  E2= 90, line drawn from centre to midpoint of chord

     hence, BAC=E2

Therefore BA I I OD

2. A1=x

B=x, tan-chord

O1=x, corresp <s equal, AB parallel to OD

A1 = O1

   therefore AOCD  is a cyclic quad , converse theorem of <s in the same segment.

3. AOC =2x ,< at centre = 2 x < at circumf.

O1=x and also O2 = X

C2=O2=x, <s in same segment

   hence C2=B=x

 therefore DC is a tangent to circle, converse of ta-chord theorem
by Diamond (53,132 points)

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MathsGee Android Q&A

MathsGee Android Q&A