Consider a circle with centre at O and radius 7 cm. Let QR be a chord of length 2 cm and let P be the mid-point ofQR. Let CD be another chord of this circle passing through P such that CPQ is acute. If M is the mid-point ofCD and MP =  cm, then which of the following statements are correct?

1. QPD = 135°

2. If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x² − 10x + 1 = 0.

3. The ratio of the area of OPR to the area of OMP is 1 : 2 .

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