Institution: Directorate of Primary Education - DPE Exam: Primary Question Solution 2014 – Gama
Topic: Geometry Mathematics (জ্যামিতি), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

In a circle, when two chords intersect, the segments created by their intersection can provide important relationships. In this case, we have two equal chords, AB and CD, that intersect at point P.

According to the properties of chords in a circle, when two chords intersect, the segments formed on one chord are proportional to the segments formed on the other chord. Specifically, if we denote the segments as follows:

- PB is the segment from point P to point B on chord AB.
- PA is the segment from point P to point A on chord AB.
- PD is the segment from point P to point D on chord CD.
- PC is the segment from point P to point C on chord CD.

Since AB and CD are equal in length, this equality leads to a specific property regarding the segments. The relationship derived from the intersection of chords states that \( PB \times PA = PC \times PD \).

However, because the lengths of the chords are equal, we can infer that the segments on either side of the intersection point must also maintain balance regarding their lengths. Therefore, it follows that \( PB \) is equal to \( PD \), confirming option A, which states \( PB = PD \).

This property holds true regardless of the specific lengths of segments PA, PB, PC, or PD, so option A is indeed the correct and validated choice.