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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» <html><body><p><strong><a href="https://interviewquestions.tuteehub.com/tag/answer-15557" style="font-weight:bold;" target="_blank" title="Click to know more about ANSWER">ANSWER</a>:</strong></p><p>Given: AB and AC are two equal chords of a <a href="https://interviewquestions.tuteehub.com/tag/circle-916533" style="font-weight:bold;" target="_blank" title="Click to know more about CIRCLE">CIRCLE</a> with centre O.</p><p>OP⊥AB and OQ⊥AC.</p><p>To prove: PB=QC</p><p>Proof: OP⊥AB</p><p>⇒AM=MB .... (perpendicular from centre bisects the chord)....(i)</p><p><a href="https://interviewquestions.tuteehub.com/tag/similarly-1208242" style="font-weight:bold;" target="_blank" title="Click to know more about SIMILARLY">SIMILARLY</a>, AN=NC....(ii)</p><p>But, AB=AC</p><p>⇒ </p><p>2</p><p>AB</p><p> </p><p> = </p><p>2</p><p>AC</p><p> </p><p> </p><p>⇒MB=NC ...(iii) ( From (i) and (ii) )</p><p>Also, OP=OQ (Radii of the circle)</p><p>and OM=ON (Equal chords are equidistant from the centre)</p><p>⇒OP−OM=OQ−ON</p><p>⇒MP=NQ ....(iv) (From figure)</p><p>In ΔMPB and ΔNQC, we have</p><p>∠PMB=∠QNC (Each =<a href="https://interviewquestions.tuteehub.com/tag/90-341351" style="font-weight:bold;" target="_blank" title="Click to know more about 90">90</a> </p><p>∘</p><p> )</p><p>MB=NC ( From (iii) )</p><p>MP=NQ ( From (iv) )</p><p>∴ΔPMB≅ΔQNC (SAS)</p><p>⇒PB=QC (<a href="https://interviewquestions.tuteehub.com/tag/cpct-2017971" style="font-weight:bold;" target="_blank" title="Click to know more about CPCT">CPCT</a>)</p><p><strong>Step-by-step explanation:</strong></p><p>please mark as brainliest</p></body></html>


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