Circles is one of the crucial topics of Maths. It is an important topic for Board exams for class 10(CBSE). Apart from studying and practicing problems on circles from NCERT, students shall also practice these important questions.
Solving these important questions of class 10 maths chapter 10 will help you prepare for CBSE board exams.
Question 1. A tangent AB at a point A of a circle of radius 5 cm will meet a line passing through the centre O at a point B so that OB = 12 cm. Find the length AB?
As you can see, the line drawn from the centre O of the circle to the tangent AB is ⊥ to the tangent.
∴ OA ⊥ AB
By Pythagoras theorem in ΔOAB,
OA2 = OA2 + AB2
⇒ (12)2 = 52 + AB2
⇒ AB2 = 144 – 25
⇒ AB2 = 119
⇒ AB = √119 cm
(D) is the right option.
Question 2. 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.
PQ and RS are two parallel lines.
RS is the tangent to the circle at point C
PQ is the secant to the circle
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Question 3: How many tangents can be drawn from the external point to a circle?
Answer: Two tangents can be drawn from the external point to a circle.
Question 4: Given: A triangle OAB which is an isosceles triangle and AB is tangent to the circle with center O. Find the measure of ∠OAB.
Answer: The measure of ∠OAB in the given isosceles triangle OAB will be 45 degrees.
Question 5: From point A, the length of the tangent to a circle is 24 cm and the distance of B from the centre is 25 cm. Find the radius of the circle.
Answer: The line is drawn from the centre of the circle OA to the tangent is ⊥ to the tangent.
Therefore, OA ⊥ AB
also, ΔAOB is right-angled.
OB = 25 cm and AB = 24 cm (Given)
By Pythagoras theorem in ΔAOB,
OB2 = OA2 + AB2
⇒ (25)2 = OA2 + (24)2
⇒ OA2 = 625 – 576
⇒ OA2 = 49
⇒ OA = 7 cm
The radius of the circle is an option 7 cm.
Question 6: What should be the angle between the two tangents which is drawn at the end of of two radii and are inclined at an angle of 45 degrees?
Answer: The angle between them shall be: 135 degrees.
Question 7: Given a right triangle PQR which is right angled at q. QR = 12 cm, PQ = 5 cm. The radius of the circle which is inscribed in triangle PQR will be?
Answer: The radius of the circle will be 2 cm.
Question 8: Define Tangent and Secant?
Answer: A tangent is a line which meets the circle only in one point.
A secant is a line which meets circle at two points while intersecting it. These two pints rae always distinct.
Question 9: What is circle?
Answer: If we collect all the points given on a plane and are at a constant distance, we will get a circle. The constant distance will be called as radius and the fixed point will be the centre of the circle.
Question 10. From a point B , which is 10mcm far from the centre O, a tangent AB of length 8cm is made. Calculate its radius.
Answer: If O is the centre of the circle then OA is perpendicular to AB. In right triangle OAB,
OB2 = OA2 + AB2
OA = √(AB2 – OB2) = √(102 – 82) = √36cm = 6cm.