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Question: The co-ordinates of two points P and Q are (x<sub>1</sub>, y<sub>1</sub>) and (x<sub>2</sub>, y<sub>...

The co-ordinates of two points P and Q are (x1, y1) and (x2, y2) and O is the origin. If circles be described on OP and OQ as diameters then length of their common chord is –

A

∣x1y2+x2y1∣PQ\frac{|x_{1}y_{2} + x_{2}y_{1}|}{PQ}

B

∣x1y2−x2y1∣PQ\frac{|x_{1}y_{2} - x_{2}y_{1}|}{PQ}

C

∣x1x2+y1y2∣PQ\frac{|x_{1}x_{2} + y_{1}y_{2}|}{PQ}

D

∣x1x2−y1y2∣PQ\frac{|x_{1}x_{2} - y_{1}y_{2}|}{PQ}

Answer

∣x1y2−x2y1∣PQ\frac{|x_{1}y_{2} - x_{2}y_{1}|}{PQ}

Explanation

Solution

Find area of DOPQ in two ways.