In Fig, PQ is tangent to a circle centered at O. If the radius of the circle is 5 cm, then the length of the tangent PQ is:

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

Q.
In Fig, PQ is tangent to a circle centered at O. If the radius of the circle is 5 cm, then the length of the tangent PQ is:

1 $5 \sqrt{3} c m$

2 $\frac{10}{\sqrt{3}} c m$

3 10 cm

4 $\frac{5}{\sqrt{3}} c m$

Ans.
(1)

Given, OQ = 5 cm

Since PQ is tangent to a circle with centre O, at point Q

$∴ O Q ⟂ P Q \Rightarrow ∠ O Q P = 90 ° I n r i g h t Δ O P Q, w e h a v e t a n 30 ° = \frac{O Q}{P Q} \frac{1}{\sqrt{3}} = \frac{5}{P Q} \Rightarrow P Q = 5 \sqrt{3} cm$

Solution

Q.
In Fig, PQ is tangent to a circle centered at O. If the radius of the circle is 5 cm, then the length of the tangent PQ is:

1 $5 \sqrt{3} c m$

2 $\frac{10}{\sqrt{3}} c m$

3 10 cm

4 $\frac{5}{\sqrt{3}} c m$

Ans.
(1)

Given, OQ = 5 cm

Since PQ is tangent to a circle with centre O, at point Q

$∴ O Q ⟂ P Q \Rightarrow ∠ O Q P = 90 ° I n r i g h t Δ O P Q, w e h a v e t a n 30 ° = \frac{O Q}{P Q} \frac{1}{\sqrt{3}} = \frac{5}{P Q} \Rightarrow P Q = 5 \sqrt{3} cm$

Want Us to Email you About Special Offers & Updates?

Solution

Q. In Fig, PQ is tangent to a circle centered at O. If the radius of the circle is 5 cm, then the length of the tangent PQ is:

1 53cm

2 103cm

3 10 cm

4 53cm

Ans. (1) Given, OQ = 5 cm Since PQ is tangent to a circle with centre O, at point Q ∴ OQ ⟂ PQ⇒ ∠OQP = 90°In right ΔOPQ, we havetan30°=OQPQ13=5PQ⇒PQ=53 cm

Want Us to Email you About Special Offers & Updates?

Q.
In Fig, PQ is tangent to a circle centered at O. If the radius of the circle is 5 cm, then the length of the tangent PQ is:

1 $5 \sqrt{3} c m$

2 $\frac{10}{\sqrt{3}} c m$

4 $\frac{5}{\sqrt{3}} c m$

Ans.
(1)

Given, OQ = 5 cm

Since PQ is tangent to a circle with centre O, at point Q

$∴ O Q ⟂ P Q \Rightarrow ∠ O Q P = 90 ° I n r i g h t Δ O P Q, w e h a v e t a n 30 ° = \frac{O Q}{P Q} \frac{1}{\sqrt{3}} = \frac{5}{P Q} \Rightarrow P Q = 5 \sqrt{3} cm$