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### Question Asked by a Student from EXXAMM.com Team

** Q 1730134912. ** 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 of `QR`. Let `CD` be another chord of this

circle passing through `P` such that `angleCPQ` is acute.

If `M` is the mid-point of `CD` and `MP` `= sqrt24` cm,

then which of the following statements are correct `?`

1. `angleQPD = 135^0`

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 `DeltaOPR` to the area of

`DeltaOMP` is `1 : 2sqrt2`

.

Select the correct answer using the codes given below.

**CDS 2016 **