(i)
(ii)
(iii)
(iv)
(v)
Find the unknown length x in each of the following figures.

Question

(i) (ii) (iii) (iv) (v) Find the unknown length x in each of the following figures.

KnowledgeBoat · Accepted Answer

We know that, If two chords of a circle intersect internally, then the products of the length of segments are equal. (i) PA × PB = PC × PD 5 × 5.6 = 3.5 × x x = x = 8 cm. Hence, x = 8 cm. (ii) PA × PB = PC × PD x × 9 = 8.1 × 5 x = x = 4.5 cm Hence, x = 4.5 cm. We know that, If two chords of a circle intersect externally, then the products of the length of segments are equal. (iii) PA × PB = PC × PD ⇒ PB = PA + AB = 7 + 9 = 16 ⇒ PD = PC + CD = 8 + x ⇒ 7 × 16 = 8 × (8 + x) ⇒ 112 = 64 + 8x ⇒ 8x = 112 - 64 ⇒ x = ⇒ x = 6 cm. Hence, x = 6 cm. (iv) 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. PT2 = AP × BP x2 = 4.5 × 18 x2 = 81 x = 9 cm. Hence, x = 9 cm. (v) 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. PT2 = AP × BP ⇒ BP = AP + AB = x + 10 ⇒ 122 = x × (x + 10) ⇒ 144 = x2 + 10x ⇒ x2 + 10x - 144 = 0 ⇒ x2 + 18x - 8x - 144 = 0 ⇒ x(x + 18) - 8(x + 18) = 0 ⇒ (x - 8)(x + 18) = 0 ⇒ (x - 8) = 0 or (x + 18) = 0 [Using Zero-product rule] ⇒ x = 8 or x = -18 x = 8 because length cannot be negative. Hence, x = 8 cm.

Mathematics

(i)
(ii)
(iii)
(iv)
(v)
Find the unknown length x in each of the following figures.

Circles

Related Questions

In the given figure, O is the centre of the circle. PQ and PR are tangents and ∠QPR = 70°. Calculate :
(i) ∠QOR
(ii) ∠QSR

In the given figure, O is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26°, then find :
(i) ∠BDA
(ii) ∠BAD
(iii) ∠CAD
(iv) ∠ODB

Two chords AB and CD of a circle intersect externally at E. If EC = 2 cm, EA = 3 cm and AB = 5 cm, find the length of CD.

In the adjoining figure, PT is a tangent to the circle. Find PT, if AP = 16 cm and AB = 12 cm.

Mathematics

(i)(ii)(iii)(iv)(v)Find the unknown length x in each of the following figures.

Circles

Related Questions

In the given figure, O is the centre of the circle. PQ and PR are tangents and ∠QPR = 70°. Calculate :(i) ∠QOR(ii) ∠QSR

In the given figure, O is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26°, then find :(i) ∠BDA(ii) ∠BAD(iii) ∠CAD(iv) ∠ODB

Two chords AB and CD of a circle intersect externally at E. If EC = 2 cm, EA = 3 cm and AB = 5 cm, find the length of CD.

In the adjoining figure, PT is a tangent to the circle. Find PT, if AP = 16 cm and AB = 12 cm.

(i)
(ii)
(iii)
(iv)
(v)
Find the unknown length x in each of the following figures.

In the given figure, O is the centre of the circle. PQ and PR are tangents and ∠QPR = 70°. Calculate :
(i) ∠QOR
(ii) ∠QSR

In the given figure, O is the centre of the circle. CE is a tangent to the circle at A. If ∠ABD = 26°, then find :
(i) ∠BDA
(ii) ∠BAD
(iii) ∠CAD
(iv) ∠ODB