PQ is a chord of length 8 cm of a circle of radius 5 cm. the tangents at P and Q intersect at a point T. What is the length of the tangent PT ? एक 5 सेमी त्रिज्या वाले वृत्त की जीवा PQ की लम्बाई 8 सेमी है। P और PQ पर स्पर्श रेखायें बिन्दु T पर प्रतिच्छेदित करती हैं। स्पर्श रेखा PT की लम्बाई ज्ञात करो ?

Using the property that tangents from an external point are equal, and the right triangle formed by radius, half-chord, and tangent: Distance from center to chord = √(5² - 4²) = 3 cm. By similar triangles or power of a point theorem, PT = 5²/3 = 25/3, but more accurately, using the formula PT² = d² - r² where d is distance from T to center: PT = 20/3 cm.