Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
Exam Preparedness: Sample Question Papers provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
Sample Questions
Sec A
(1) The number of common tangents can be drawn to two concentric circles is ................
(2) In a circle, 'O' is the centre, P is the external point and AP is the tangent drawn to the circle from P, OA is the radius. If ∠APO = 30°, then ∠POA = ?
(A) 120° (B) 90° (C) 30° (D) 60°
(3) 'O' is the centre. PA and PB are tangents drawn to the circle from point P. If angle between the tangents is 60° and length of the tangent is
(A) 2 cm (B) 1 cm
(C)
(4) The number of secants can be drawn to a circle from an external point is ......
(A) Infinite (B) 1
(C) 2 (D) 0
(5) The length of the tangent to a circle from a point 17 cm from its centre is 8 cm. Find the radius of the circle.
(6) A point P is 25 cm from the centre O of the circle. The length of the tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
Sec B
(1) In the given figure, 'O' is the centre of a circle, OQ is the radius and OQ = 5 cm. The length of the tangent drawn from external point to the circle PQ = 12 cm, then find the distance between the points 'O' and 'P'.
(2) Draw a circle and two lines parallel to a given line such that one is a tangent and the other is a secant to the circle.
(3) AOB is the diameter of a circle with centre 'O' and AC is a tangent to the circle at A. If ∠BOC = 130°, then find ∠ACO.
(4) In the given figure, TA and TB are tangents to the circle with centre 'O'. If ∠ATB = 80°, then find the measure of ∠ABT.
Sec C
(1) Draw a circle of radius 3 cm. Construct a pair of tangents to the circle from an external point which is at a distance of 8 cm from the centre of the circle.
(2) Draw a circle of radius 4 cm. From a point 9 cm away from it's centre, construct a pair of tangents to the circle.