Five mark exercise problem IV — task. Mathematics State Board, Class 10.

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Two triangles \(QPR\) and \(QSR\), right angled at \(P\) and \(S\) respectively are drawn on the same base \(QR\) and on the same side of \(QR\). If \(PR\) and \(SQ\) intersect at \(T\), prove that \(PT \times TR = ST \times TQ\).

Answer:

In \(\Delta PTQ\) and \(\Delta STR\):

∠ QPT = ∠ i

∠ PTQ = ∠ i

Therefore, \(\Delta PTQ\) \(\Delta STR\).

\frac{PT}{i} = \frac{i}{RT}

i \times i = i \times i

Hence, it is proved.

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23. Five mark exercise problem IV

Exercise condition: