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Two chords AB, CD of a circle intersect externally at a point P. If PB = 7 cm, AB = 9 cm and PD = 6 cm, find CD.

Circles

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Answer

We know that,

If two chords of a circle intersect externally, then the products of the length of segments are equal.

From figure,

Two chords AB, CD of a circle intersect externally at a point P. If PB = 7 cm, AB = 9 cm and PD = 6 cm, find CD. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

PA.PB = PC.PD …..(i)

PA = PB + AB = 7 + 9 = 16 cm.

Putting values in equation (i) we get,

⇒ 16 × 7 = PC × 6
⇒ 112 = PC × 6
⇒ PC = 1126\dfrac{112}{6}

⇒ PC = 563\dfrac{56}{3}.

From figure,

CD = PC - PD = 563−6=56−183=383=1223.\dfrac{56}{3} - 6 = \dfrac{56 - 18}{3} = \dfrac{38}{3} = 12\dfrac{2}{3}.

Hence, the value of CD = 122312\dfrac{2}{3} cm.

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