Question

C is the centre of a circle with radius 8 cm. P is a point outside the circle and PA is the tangent of the circle
Find:
I) the length of tangent PA , if CP= 10 cm
ll) the distance between C and P , if the length of the tangent PA is 15cm

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Answer 1

Step-by-step explanation:

(i)

radius=r=8 cm

distance between centre and the point =d=10cm

PA=

$\sqrt{ {d}^{2} - {r}^{2} }$

$\sqrt{ {10}^{2} - {8}^{2} }$

$\sqrt{100 - 64}$

$\sqrt{36}$

=6cm

(ii)

radius=r=8 cm

CP= d=?

PA=15cm

15=

$\sqrt{ {d}^{2} - {8}^{2} }$

squaring on both sides

225=

${d}^{2} - {8}^{2}$

225+64=

${d}^{2}$

=289

d=17cm

CP=17cm

Answer 2

Answer:

(i)

radius=r=8 cm

distance between centre and the point =d=10cm

PA=

\sqrt{ {d}^{2} - {r}^{2} }

d

2

−r

2

\sqrt{ {10}^{2} - {8}^{2} }

10

2

−8

2

\sqrt{100 - 64}

100−64

\sqrt{36}

36

=6cm

(ii)

radius=r=8 cm

CP= d=?

PA=15cm

15=

\sqrt{ {d}^{2} - {8}^{2} }

d

2

−8

2

squaring on both sides

225=

{d}^{2} - {8}^{2}d

2

−8

2

225+64=

{d}^{2}d

2

=289

d=17cm

CP=17cm