# Class 10 RD Sharma Solutions – Chapter 10 Circles – Exercise 10.1

Last Updated : 13 Jan, 2021

### (i) The common point of a tangent and the circle is called â€¦â€¦â€¦.

Solution:

Point of contact.

Solution:

Two

Solution:

One

Solution:

Secant

### (v) The angle between tangent at a point on a circle and the radius through the point is â€¦â€¦â€¦..

Solution:

Right angle (90Â°)

### Question 2. How many tangents can a circle have?

Solution:

Tangent is a line that intersect a circle at only point. Since there are a infinite number of points on a circle, a circle can have infinite tangents.

### Question 3. O is the centre of a circle of radius 8 cm. The tangent at a point A on the circle cuts a line through O at B such that AB = 15 cm. Find OB.

Solution:

AB = 15 cm

OA âŠ¥ tangent AB

Therefore, In right âˆ†OAB, by applying Pythagoras Theorem:

OBÂ² = OAÂ² + ABÂ²

=> OBÂ² = (8)Â² + (15)Â²

= 64 + 225 = 289 = (17)Â²

=> OB = 17 cm

Thus, OB = 17 cm

### Question 4. If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

Solution:

OQ = 25 cm

PQ = 24 cm

OP âŠ¥ tangent PQ

therefore, In right âˆ†OPQ, by applying Pythagoras Theorem:

OQÂ² = OPÂ² + PQÂ²

=> (25)Â² = OPÂ² + (24)Â²

=> 625 = OPÂ² + 576

=> OPÂ² = 625 â€“ 576 = 49

=> OPÂ² = (7)Â²

OP = 7 cm

Thus, radius of the circle is 7 cm

Previous Article
Next Article
Article Tags :