NCERT Solutions for Class 10 Maths Chapter 10 – Circles
Exercise: 10.1
1. How many tangents can a circle have?
Answer
A circle can have infinite tangents.
2. Fill in the blanks :
(i) A tangent to a circle intersects it in ............... point(s).
(ii) A line intersecting a circle in two points is called a .............
(iii) A circle can have ............... parallel tangents at the most.
(iv) The common point of a tangent to a circle and the circle is called ............
Answer
(i) one
(ii) secant
(iii) two
(iv) point of contact
3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at
a point Q so that OQ = 12 cm. Length PQ is :
a point Q so that OQ = 12 cm. Length PQ is :
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D) √119 cm
(B) 13 cm
(C) 8.5 cm
(D) √119 cm
Answer
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQOZ-oayOcqqdicRF6U5fv-Ah85GZ06HtIx9Cfvi3KnhtyUfxT297aieCeAvqwrKsOSjb8YzUYobhk-Z5YgK3-5CJCcT35KJO_VMvbj4b9kLR1YpGA6oC23DusV-ls_7QTTRXaPY1Wy9I/s1600/ch10-circles-class10-1.png)
∴ OP ⊥ PQ
By Pythagoras theorem in ΔOPQ,
OQ2 = OP2 + PQ2
⇒ (12)2 = 52 + PQ2
⇒ (12)2 = 52 + PQ2
⇒PQ2 = 144 - 25
⇒PQ2 = 119
⇒PQ = √119 cm
(D) is the correct option.
4. Draw a circle and two lines parallel to a given line such that one is a tangent and the
other, a secant to the circle.
Answer
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4CASFeK4ZzdLPjGe5o8_PqFtEjxTIbWRqsll8FdnKOOnDYtvMS1_NhqK1O8qWjlg0RUQoEaYN3ZMx6nOpyv7d68OmH_-SthkqNp0t2cPASFXl9iFH1fa4sWC3PgeEBz0FEGJXIyBZgg0/s1600/ch10-circles-class10-2.png)
AB and XY are two parallel lines where AB is the tangent to the circle at point C while XY is the secant to the circle.
![](https://farm9.staticflickr.com/8014/7652595764_2957a4bcd5_o.jpg)
![](https://farm9.staticflickr.com/8026/7652597890_074e5134dd_o.jpg)
![](https://farm9.staticflickr.com/8167/7652598482_b1faa983b3_o.jpg)
![](https://farm8.staticflickr.com/7266/7652598166_9822be5765_o.jpg)
![](https://farm9.staticflickr.com/8424/7652598788_987394df62_o.jpg)
![](https://farm8.staticflickr.com/7278/7652599116_8759c88d07_o.jpg)
![](https://farm8.staticflickr.com/7259/7652599348_099506771f_o.jpg)
![](https://farm9.staticflickr.com/8431/7652599988_da4877e63c_o.jpg)
![](https://farm9.staticflickr.com/8162/7652599666_8cbef59996_o.jpg)
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![](https://farm9.staticflickr.com/8163/7652596454_34baf7e061_o.jpg)
![](https://farm8.staticflickr.com/7132/7652596770_7bea69f3da_o.jpg)
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![](https://farm8.staticflickr.com/7108/7652597360_2fca54c1b1_o.jpg)
![](https://farm8.staticflickr.com/7257/7652597626_d66a9c3472_o.jpg)