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.
(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