RD Sharma Solutions Chapter 10 Circles Exercise 10.1 Class 10 Maths
Chapter Name | RD Sharma Chapter 10 Circles |
Book Name | RD Sharma Mathematics for Class 10 |
Other Exercises |
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Related Study | NCERT Solutions for Class 10 Maths |
Exercise 10.1 Solutions
1. Fill in the blanks
(i) The common point of tangent and the circle is called point of contact.
(ii) A circle may have two parallel tangents.
(iii) A tangent to a circle intersects it in one point.
(iv) A line intersecting a circle in two points A called a secant.
(v) The angle between tangent at a point P on circle and radius through the point is 90° .
Solution
2. How many tangents can a circle have ?
Solution
Tangent: A line intersecting circle in one point is called a tangent. 
As there are infinite number of points on the circle a circle has many (infinite) tangents.
3. O is the center 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
Consider a circle with center O and radius OA = 8 cm = r, AB = 15 cm
(AB) tangent is drawn at A(point of contact)
At point of contact, we know that radius and tangent are perpendicular.
In ΔOAB, ∠OAB = 90°, By Pythagoras theorem 
4. If the tangent at point P to the circle with center O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of circle.
Solution
Given,
PQ = 24 cm
OQ = 25 cm
OP = radius = ? 
P is point of contact, At point of contact, tangent and radius are perpendicular to each other
∴ΔPOQ is right angled triangle ∠OPQ = 90°
By Pythagoras theorem, 