Question

If PA and PB are tangents to the circle
at A and B respectively and the chord BC
is parallel to the tangent PA , If AC is 6
cm and the length of the tangent AP is 9
cm. Then what is the length of the chord
BC?
a) 4 b)5
c) 6 d)87.; If PA and PB are tangents to the circle; at A and B respectively and the chord BC; is parallel to the tangent PA , If AC is 6; cm and the length of the tangent AP is 9; cm. Then what is the length of the chord; BC?; a) 4 b)5; c) 6 d)87.

Answer 1

Answer:

Step-by-step explanation:

PA=PB=9cm ( Length of tangents from external point)

∠PAB = ∠ABC (Alternate angle)

AC=AB=6cm

▵PAB and ▵ACB are isosceles and similar triangle.

Taking ratio of respective sides,

BC/AB = AC/PB

⇒ BC/6 = 6/9

∴ BC = 4cm.

Answer 2

Answer:

Step-by-step explanation:

Given:

PA and PB are tangents to the circle at A and B respectively.

Also, PA$=9 cm$

We know that,

The length of tangents from an external point to a circle are equal.

⇒PA=PB=9cm

Given,

The chord BC is parallel to the tangent PA.

⇒∠PAB = ∠ABC (Alternate angle)

⇒AC=AB=6cm

Hence, ΔPAB and ΔACB are isosceles and similar triangles.

Taking the ratio of respective sides of the triangles,

$\frac{BC}{AB} =\frac{AC}{PB}$

⇒ $\frac{BC}{6} =\frac{6}{9}$

⇒$BC=\frac{36}{9}$

⇒BC = $4$ cm

Hence, the length of the chord BC is $4$ cm.