What is the ratio PR - RQ for the following construction method-1- A ray is extended from P and 11 arcs of equal lengths are cut- cutting the ray at P 1- P 2- P 11-2- A line is drawn from P 11 to Q and a line parallel to P 11 Q is drawn- passing through the point P 7 which meets PQ at R-A- 13- 30B- 13- 17C- 17- 30D- 17- 13

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What is the r...

Question

What is the ratio $\frac{P R}{R Q}$ for the following construction method?

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Solution

The correct option is B
17:13

Here the total number of arcs is equal to m+n in the ratio m:n.

The triangles $△ P P_{7} R$ and $△ P P_{11} Q$ are similar.

Hence, $\frac{P R}{P Q} = \frac{P P_{7}}{P P_{11}} = \frac{7}{11}$

$1 = \frac{P Q}{P Q} = \frac{P R}{P Q} + \frac{R Q}{P Q}$

Hence, $\frac{Q R}{P Q} = \frac{4}{11}$

$\frac{P R}{Q R} = \frac{\frac{P R}{P Q}}{\frac{Q R}{P Q}} = \frac{7}{4}$

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What is the ratio PRRQ for the following construction method?

The correct option is B 17:13 Here the total number of arcs is equal to m+n in the ratio m:n. The triangles △PP7R and △PP11Q are similar. Hence, PRPQ=PP7PP11=711 1=PQPQ=PRPQ+RQPQ Hence, QRPQ=411 PRQR=PRPQQRPQ=74

What is the ratio $\frac{P R}{R Q}$ for the following construction method?