Question

O is an centre of a circle. P is an external point of it at distance of 13cm from O. The radius of the circle is 5cm. Then the length of a tangent to the circle from P upto the point of contact is

A) √194cm B) 10cm C) 12cm D) 8cm

Answer 1

Answer:

8 is the right answer

Because the formula is 2pier

Answer 2

Question:

O is a centre of a circle. P is an external point of it at distance of 13 cm from O. The radius of the circle is 5 cm. Then the length of a tangent to the circle from P upto the point of contact is

A) √194 cm

B) 10 cm

C) 12 cm

D) 8 cm

Answer:

C) 12 cm

Given:

⇛O is a centre of a circle.

⇛P is an external point of it at distance of 13cm.

from O.

⇛The radius of the circle is 5cm.

To Find:

The length of a tangent to the circle from P upto the point of contact .

Solution:

( refer the attachment )

According to the question,

OP = 13 cm

OR = 5 cm

∠ORP = 90°

(∵ line drawn on tangent form center made an angle of 90∘ with tangent. )

➞RP² = OP² - OR²

➞RP² = ( 13 )² - ( 5 )²

➞RP² = 169 - 25

➞RP² = 144

➞RP² = ( √12 )²

⛬ RP = 12

The length of a tangent to the circle from P upto the point of contact = 12 cm.

Therefore, option B) 12 cm is correct.