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Two Similar Triangles, ISI Entrance Subjective 2018

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Understand the problem

[/et_pb_text][et_pb_text _builder_version="3.27.4" text_font="Raleway||||||||" background_color="#f4f4f4" custom_margin="10px||10px" custom_padding="10px|20px|10px|20px" box_shadow_style="preset2"]Suppose that \(PQ\) and \(RS\) are two chords of a circle intersecting at a point \(O\) , It is given that \(PO=3\) cm and \( SO=4\) cm . Moreover, the area of the triangle \(POR\) is \(7 cm^2 \) . Find the are of the triangle \(QOS\) .  

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I.S.I. (Indian Statistical Institute) B.Stat/B.Math Entrance Examination 2018. Subjective Problem no. 2.
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Plane Geometry [/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="3.22.4" open="off"]

5.5 out of 10

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'Challenge and Thrill of Pre-College Mathematics' by V,Krishnamurthy, C.R.Pranesachar, ect.

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Start with hints

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Do you really need a hint? Try it first!

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\(PQ\) and \( RS\) are two chords of the circle \(C\) , intersecting at the point \(O\). See figure: click here.

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Given \(PO=3\) cm \(SO=4\) cm \([\triangle POR]= 7 cm^2\).  

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From the triangles \(POS\) and \(QOS\) we have,                 \(\angle POR=\angle SOQ\) [Opposite angles]                 \(\angle SRP=\angle SQO \) [Angle on the same semi-circle \(STP\)]                 \(\angle QSO= \angle OPR\) [Angle on the same semi-circle \(ST'P\)]  Therefore the \(\triangle POR\) and \(\triangle SOQ\) are similar triangles .  

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\(\frac{[\triangle POR]}{OP^2}=\frac{[\triangle SOQ]}{SO^2}.\) \(\Rightarrow [\triangle SOQ]=\frac{SO^2}{PO^2}\cdot [\triangle POR]\)=\(\frac{4^2}{3^2}\cdot 7=12\frac{4}{9}\).(Ans.)

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Connected Program at Cheenta

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Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.

The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.

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Similar Problem

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