PR is tangent to a circle, with centre O and radius 4 cm., at point Q. If ∠POR = 90o, OR = 5 cm. and OP = 20/3 cm., then in the cm., the length of PR is - O केन्द्र और 4 सेमी. त्रिज्या वाले एक वृत्त के Q बिन्दु पर PR एक स्पर्श रेखा है। तदनुसार यदि ∠POR = 90o, OR = 5 सेमी. और OP = 20/3 सेमी. हो तो PR की लम्बाई कितने सेमी. होगी?

Since PR is tangent at Q, OQ ⟂ PR and OQ = 4 cm. Using Pythagoras in right triangles OQP and OQR: PQ² = OP² - OQ² = (400/9) - 16 = 256/9, so PQ = 16/3. QR² = OR² - OQ² = 25 - 16 = 9, so QR = 3. Therefore PR = PQ + QR = 16/3 + 3 = 25/3 cm. Alternatively, using properties of right triangles and the given that ∠POR = 90°, the altitude from Q to hypotenuse PR in right triangle POR satisfies (PQ)(QR) = OQ², which gives the same result.