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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
now in ΔORE
by Pythagoras theorem,
radius , OR² = OE² +ER²
                     = 12.75 + 12.25 = 25
∴OR² =25
radius , OR = 5 cm
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