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A point p is outside at a distance of 13 cm from its center . a secant from p cuts the circle in Q and R such that QR =7cm and the segment PQ of the secant

exterior to the circle is 9cm therefore the radius of circle

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Let the center be O draw perpendicular to the secant, cuts at E now in ΔOEP OP = 13 cm EP = 3.5 + 9 = 12.5 cm so, by Pythagoras theorem, OE² = OP² - EP² =(13)² - (12.5)² = 169 - 156.25 =12.75 now in ΔORE by Pythagoras theorem, radius , OR² = OE² +ER² = 12.75 + 12.25 = 25 ∴OR² =25 radius , OR = 5 cm