Class 10 RD Sharma Solutions – Chapter 10 Circles – Exercise 10.1
Question 1. Fill in the blanks :
(i) The common point of a tangent and the circle is called ……….
Point of contact.
Attention reader! All those who say programming isn't for kids, just haven't met the right mentors yet. Join the Demo Class for First Step to Coding Course, specifically designed for students of class 8 to 12.
The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.
(ii) A circle may have ………. parallel tangents.
(iii) A tangent to a circle intersects it in ……….. point(s).
(iv) A line intersecting a circle in two points is called a …………
(v) The angle between tangent at a point on a circle and the radius through the point is ………..
Right angle (90°)
Question 2. How many tangents can a circle have?
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.
Radius OA = 8 cm
AB = 15 cm
OA ⊥ tangent AB
Therefore, In right ∆OAB, by applying Pythagoras Theorem:
OB² = OA² + AB²
=> OB² = (8)² + (15)²
= 64 + 225 = 289 = (17)²
=> 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.
OP is the radius
OQ = 25 cm
PQ = 24 cm
OP ⊥ tangent PQ
therefore, In right ∆OPQ, by applying Pythagoras Theorem:
OQ² = OP² + PQ²
=> (25)² = OP² + (24)²
=> 625 = OP² + 576
=> OP² = 625 – 576 = 49
=> OP² = (7)²
OP = 7 cm
Thus, radius of the circle is 7 cm