AB is a diameter of a circle and PT is a tangent at point T to circle from an external point P. Find the value of PA if AB = 7 units and PT = 12 units. एक वृत्त का एक व्यास AB है और एक वाह्य बिन्दु P से वृत्त पर बिन्दु T पर एक स्पर्श रेखा PT है। PA का मान ज्ञात कीजिए यदि AB = 7 मात्रक और PT = 12 मात्रक है।

For any circle, if AB is a diameter and PT is a tangent from external point P, then PT² = PA × PB. This is the power of a point theorem. Given AB = 7, PT = 12. Let PA = x, then PB = PA + AB = x + 7. So: 12² = x(x + 7). 144 = x² + 7x. x² + 7x - 144 = 0. (x + 16)(x - 9) = 0. Therefore x = 9. Option A (7) would be the diameter itself, not PA.