Answer
423.9k+ views
Hint: We know that tangent is always perpendicular to the radius made from that point, using this point we’ll use the property of right-angled triangle so formed.
After using the property we’ll get an equation and solving that equation we’ll get the value of the radius of the circle.
Complete step-by-step answer:
Given data: \[Length{\text{ }}of{\text{ }}tangent = 8cm\]
The distance of the point from centre=17cm
Let the centre of the circle be ‘O’ and the point from which the tangent is made be ‘R’, the point tangent touches the circle be ‘P’.
We know that tangents are always perpendicular to the radius made from that point.
Therefore, \[OP \bot PR\] or $\angle P = {90^ \circ }$
Using Pythagoras theorem
i.e., in a right-angled triangle ABC with right angle at A, $B{C^2} = A{B^2} + C{A^2}$
Therefore, Using Pythagoras theorem in triangle OPR where $\angle P = {90^ \circ }$
$ \Rightarrow O{R^2} = P{R^2} + P{O^2}$
Substituting the value of OR and PR
$ \Rightarrow {17^2} = {8^2} + P{O^2}$
On Separating the unknown term,
$ \Rightarrow P{O^2} = {17^2} - {8^2}$
On squaring we get,
$ \Rightarrow P{O^2} = 289 - 64$
$ \Rightarrow P{O^2} = 225$
Taking positive square root on both sides, we get,
$\therefore PO = 15cm$
Therefore, the radius of the circle is 15 cm.
Note: Here we have given the tangent of the circle, so let us discuss some properties related to the tangent of a circle
1.A tangent of a circle always touches the circle at a single point.
2.Tangent is always perpendicular to the radius made at the point of tangency.
3.The length of two tangents drawn to a single point to a circle is always equal.
After using the property we’ll get an equation and solving that equation we’ll get the value of the radius of the circle.
Complete step-by-step answer:
Given data: \[Length{\text{ }}of{\text{ }}tangent = 8cm\]
The distance of the point from centre=17cm
Let the centre of the circle be ‘O’ and the point from which the tangent is made be ‘R’, the point tangent touches the circle be ‘P’.
![seo images](https://www.vedantu.com/question-sets/a714e742-e0ae-417d-8dd8-0b32dee9f37f594719579015260990.png)
We know that tangents are always perpendicular to the radius made from that point.
Therefore, \[OP \bot PR\] or $\angle P = {90^ \circ }$
Using Pythagoras theorem
i.e., in a right-angled triangle ABC with right angle at A, $B{C^2} = A{B^2} + C{A^2}$
Therefore, Using Pythagoras theorem in triangle OPR where $\angle P = {90^ \circ }$
$ \Rightarrow O{R^2} = P{R^2} + P{O^2}$
Substituting the value of OR and PR
$ \Rightarrow {17^2} = {8^2} + P{O^2}$
On Separating the unknown term,
$ \Rightarrow P{O^2} = {17^2} - {8^2}$
On squaring we get,
$ \Rightarrow P{O^2} = 289 - 64$
$ \Rightarrow P{O^2} = 225$
Taking positive square root on both sides, we get,
$\therefore PO = 15cm$
Therefore, the radius of the circle is 15 cm.
Note: Here we have given the tangent of the circle, so let us discuss some properties related to the tangent of a circle
1.A tangent of a circle always touches the circle at a single point.
2.Tangent is always perpendicular to the radius made at the point of tangency.
3.The length of two tangents drawn to a single point to a circle is always equal.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)