# O and radius 7 cm, Let QR be a chord of length 2 cm and let P be the midpoint of QR

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 midpoint of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. If M is the midpoint of CD and MP = √24 cm, then which of the following statements are correct?

1. ∠QPD = 150^{o}

2. If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x^{2} – 10x + 1 = 0

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

Select the correct answer using the code given below.

(a) 1 and 2 only

(b) 2 and 3 only

(c) 1 and 3 only

(d) 1, 2 and 3