In the figure 'o' is the centre of the circle . IF AB=BC .Prove that a

1.	In the figure 'o' is the centre of the circle . IF AB=BC .Prove that angle AOB = angle BOC . If OA= AB=BC, then find the volume of Angle AOB and angle BOC ? Find out how many equilateral triangles can be drawn in a circle with length of its side is radius
Answer» ANSWER: Given: AB and AC are two equal chords of a CIRCLE with centre O. OP⊥AB and OQ⊥AC. To prove: PB=QC Proof: OP⊥AB ⇒AM=MB .... (perpendicular from centre bisects the chord)....(i) SIMILARLY, AN=NC....(ii) But, AB=AC ⇒ 2 AB = 2 AC ⇒MB=NC ...(iii) ( From (i) and (ii) ) Also, OP=OQ (Radii of the circle) and OM=ON (Equal chords are equidistant from the centre) ⇒OP−OM=OQ−ON ⇒MP=NQ ....(iv) (From figure) In ΔMPB and ΔNQC, we have ∠PMB=∠QNC (Each =90 ∘ ) MB=NC ( From (iii) ) MP=NQ ( From (iv) ) ∴ΔPMB≅ΔQNC (SAS) ⇒PB=QC (CPCT) Step-by-step explanation: please mark as brainliest

In the figure 'o' is the centre of the circle . IF AB=BC .Prove that angle AOB = angle BOC . If OA= AB=BC, then find the volume of Angle AOB and angle BOC ? Find out how many equilateral triangles can be drawn in a circle with length of its side is radius

Answer»

Given: AB and AC are two equal chords of a CIRCLE with centre O.

OP⊥AB and OQ⊥AC.

To prove: PB=QC

Proof: OP⊥AB

⇒AM=MB .... (perpendicular from centre bisects the chord)....(i)

SIMILARLY, AN=NC....(ii)

But, AB=AC

⇒

⇒MB=NC ...(iii) ( From (i) and (ii) )

Also, OP=OQ (Radii of the circle)

and OM=ON (Equal chords are equidistant from the centre)

⇒OP−OM=OQ−ON

⇒MP=NQ ....(iv) (From figure)

In ΔMPB and ΔNQC, we have

∠PMB=∠QNC (Each =90

∘

)

MB=NC ( From (iii) )

MP=NQ ( From (iv) )

∴ΔPMB≅ΔQNC (SAS)

⇒PB=QC (CPCT)

Step-by-step explanation:

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