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Method B3

Sometimes we can prove that two lines are equal by proving that they form an isosceles triangle, ie a triangle with two equal angles. We use this heuristic here, by, first, drawing the construction line PF.

In the triangle PQF, can we show that angle P = angle F ?
We have marked some other angles that might help.

You might want to explore the situation further using the JAVA-worksheet. This allows you to move P and also to change the size of the circles.