In the figure (ii) given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find : (i) AB (ii) the length of tangent PT.

We know that, If a chord and a tangent intersect externally, then the product of lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection. ∴ TP 2 = PC × PD From figure, PC = PD + CD = 5 + 7.8 = 12.8 cm. ⇒ TP 2 = 12.8 × 5 ⇒ TP 2 = 64 ⇒ TP = ⇒ TP = 8 cm. Similarly, ⇒ TP 2 = AP × BP ⇒ 8 2 = AP × 4 ⇒ 64 = 4AP ⇒ AP = ⇒ AP = 16 cm. (i) From figure, AB = AP - BP = 16 - 4 = 12 cm. Hence, the length of AB = 12 cm. (ii) The length of tangent PT = 8 cm.

PAB is a secant and PT is tangent to a circle. If
(i) PT = 8 cm and PA = 5 cm, find the length of AB.
(ii) PA = 4.5 cm and AB = 13.5 cm, find the length of PT.

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Two chords AB, CD of a circle intersect internally at a point P. If
(i) AP = 6 cm, PB = 4 cm and PD = 3 cm, find PC.
(ii) AB = 12 cm, AP = 2 cm, PC = 5 cm, find PD.
(iii) AP = 5 cm, PB = 6 cm and CD = 13 cm, find CP.

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In the figure (i) given below, PT is a tangent to the circle. Find TP if AT = 16 cm and AB = 12 cm.

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In the adjoining figure, CBA is a secant and CD is tangent to the circle. If AB = 7 cm and BC = 9 cm, then
(i) Prove that △ACD ~ △DCB
(ii) find the length of CD.

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Mathematics

In the figure (ii) given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find :
(i) AB
(ii) the length of tangent PT.

Circles

Related Questions

PAB is a secant and PT is tangent to a circle. If
(i) PT = 8 cm and PA = 5 cm, find the length of AB.
(ii) PA = 4.5 cm and AB = 13.5 cm, find the length of PT.

Two chords AB, CD of a circle intersect internally at a point P. If
(i) AP = 6 cm, PB = 4 cm and PD = 3 cm, find PC.
(ii) AB = 12 cm, AP = 2 cm, PC = 5 cm, find PD.
(iii) AP = 5 cm, PB = 6 cm and CD = 13 cm, find CP.

In the figure (i) given below, PT is a tangent to the circle. Find TP if AT = 16 cm and AB = 12 cm.

In the adjoining figure, CBA is a secant and CD is tangent to the circle. If AB = 7 cm and BC = 9 cm, then
(i) Prove that △ACD ~ △DCB
(ii) find the length of CD.

Mathematics

In the figure (ii) given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find :(i) AB(ii) the length of tangent PT.

Circles

Related Questions

PAB is a secant and PT is tangent to a circle. If(i) PT = 8 cm and PA = 5 cm, find the length of AB.(ii) PA = 4.5 cm and AB = 13.5 cm, find the length of PT.

Two chords AB, CD of a circle intersect internally at a point P. If(i) AP = 6 cm, PB = 4 cm and PD = 3 cm, find PC.(ii) AB = 12 cm, AP = 2 cm, PC = 5 cm, find PD.(iii) AP = 5 cm, PB = 6 cm and CD = 13 cm, find CP.

In the figure (i) given below, PT is a tangent to the circle. Find TP if AT = 16 cm and AB = 12 cm.

In the adjoining figure, CBA is a secant and CD is tangent to the circle. If AB = 7 cm and BC = 9 cm, then(i) Prove that △ACD ~ △DCB(ii) find the length of CD.

In the figure (ii) given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find :
(i) AB
(ii) the length of tangent PT.

PAB is a secant and PT is tangent to a circle. If
(i) PT = 8 cm and PA = 5 cm, find the length of AB.
(ii) PA = 4.5 cm and AB = 13.5 cm, find the length of PT.

Two chords AB, CD of a circle intersect internally at a point P. If
(i) AP = 6 cm, PB = 4 cm and PD = 3 cm, find PC.
(ii) AB = 12 cm, AP = 2 cm, PC = 5 cm, find PD.
(iii) AP = 5 cm, PB = 6 cm and CD = 13 cm, find CP.

In the adjoining figure, CBA is a secant and CD is tangent to the circle. If AB = 7 cm and BC = 9 cm, then
(i) Prove that △ACD ~ △DCB
(ii) find the length of CD.