Mathematics
If AB and CD are two chords of a circle which when produced meet at a point P outside the circle such that PA = 12 cm, AB = 4 cm and CD = 10 cm, find PD.
Answer
We know that,
If two chords of a circle intersect externally, then the products of the length of segments are equal.
PA × PB = CP × PD ……..(1)
PB = PA - AB
PB = 12 - 4 = 8 cm
Let length of PD be x.
PC = x + CD = x + 10
Substituting values in equation (1) we get,
⇒ 12 × 8 = (x + 10) × x
⇒ 96 = x2 + 10x
⇒ x2 + 10x - 96 = 0
⇒ x2 + 16x - 6x - 96 = 0
⇒ x(x + 16) - 6(x + 16) = 0
⇒ (x - 6)(x + 16) = 0
⇒ x = 6 [Length cannot be negative]
⇒ PD = 6 cm.
Hence, PD = 6 cm.
Related Questions
In the adjoining figure, PT is a tangent to the circle. Find PT, if AP = 16 cm and AB = 12 cm.
Two chords AB and CD of a circle intersect at a point P inside the circle such that AB = 12 cm, AP = 2.4 cm and PD = 7.2 cm. Find CD.
In the given figure, two circles intersect each other at the points A and B. If PQ and PR are tangents to these circles from a point P on AB produced, show that PQ = PR.
In the given figure, AB is a direct common tangent to two intersecting circles. Their common chord when produced intersects AB at P. Prove that P is the mid-point of AB.
