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In the Given Figure, O Is the Centre of the Circle, Bo Is the Bisector of ∠Abc. Show That Ab = Bc. - Mathematics

Answer in Brief

In the given figure, O is the centre of the circle, BO is the bisector of ∠ABC. Show that AB = BC. 

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Solution

It is given that,∠ABC is on circumference of circle BD is passing through centre.  

Construction: Join A and C to form AC and extend BO to D such that BD be the perpendicular bisector of AC.

Now in  \[\bigtriangleup BDA \text{ and }  \bigtriangleup BDC\] we have

AD = CD           (BD is the perpendicular bisector) 

So ,

\[\angle BDA = \angle BDC = 90° \]
BD = BD  (Common)
\[\bigtriangleup BDA \cong \bigtriangleup BDC \left( \text{ SAS congruency criterion }  \right)\]
Hence AB =BC   (by cpct)
  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 15 Circles
Exercise 15.4 | Q 5 | Page 73
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