Q12 of 62 Page 193

AB and CD are two chords of a circle which when produced to meet at a point P such that AB = 5 cm, AP = 8 cm, and CD = 2 cm then PD =


Given: AB = 5 cm, AP = 8 cm, and CD = 2 cm


We know that two chords AB and CD intersect at P inside the circle with centre at O.


Then PA× PB = PC× PD.


PB =AP – AB = 8 – 5 =3 cm


Let PD = x then PC = PD + CD = 2 + x


⇒ 8 × 3 = x (2+x)


⇒ 2x +x2 =24


⇒ x2 + (6–4)x – 24 = 0


⇒ (x+6)(x –4) =0


⇒ x = 4 and –6


x = –6 is not possible because length is always positive


⇒ PD = 4 cm

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