Question

PS and RS are two chords of a circle such that PQ=10cm and RS=24 cm and PQ parallel to RS . The distance between PQ and RS is 17. Then , find the radius of the circle​

Answer 1

Step-by-step explanation:

Hence, radius of the circle is 13 cm

Answer 2

Answer:

13 cm

Step-by-step explanation:

Let

O

M

⊥

P

Q

and

O

N

⊥

R

S

.Therefore,

⇒

P

M

=

M

Q

=

10

2

=

5

c

m

and

⇒

P

N

=

S

N

=

24

2

=

12

c

m

Since,

M

N

=

17

c

m

(distance between the parallel chords), let

O

M

=

x

. Therefore,

O

N

=

17

−

x

Consider right

Δ

P

M

O

. By Pythagoras Theorem,

⇒

P

O

2

=

M

O

2

+

P

M

2

⇒

P

O

2

=

x

2

+

5

2

..(i)

Consider right

Δ

R

N

O

. By Pythagoras Theorem,

⇒

R

O

2

=

N

O

2

+

R

N

2

⇒

R

O

2

=

(

17

−

x

)

2

+

12

2

...(ii)

Since, radii of circle are equal, therefore,

P

O

2

=

R

O

2

From (i) and (ii),

⇒

x

2

+

5

2

=

(

17

−

x

)

2

+

12

2

⇒

x

2

+

25

=

289

+

x

2

−

34

x

+

144

⇒

408

=

34

x

⇒

x

=

12

∴

P

O

=

√

12

2

+

5

2

=

13cm

Hence, radius of the circle is 13 cm.