SSLC Maths - Tangents - Exam Winner Notes PDF

# SSLC Maths - Tangents - Full Chapter ## Chapter Overview - SSLC Maths - Tangents - Live session on Thu, 31 OCT at 7:30 PM - Full Chapter - Expected weightage: 21 marks ### Chapters and Weightage | No | Chapter Name | 2 marks | 3 marks | 4 marks | 5 marks | Expected weightage | |---|---|---|---...

# SSLC Maths - Tangents - Full Chapter ## Chapter Overview - SSLC Maths - Tangents - Live session on Thu, 31 OCT at 7:30 PM - Full Chapter - Expected weightage: 21 marks ### Chapters and Weightage | No | Chapter Name | 2 marks | 3 marks | 4 marks | 5 marks | Expected weightage | |---|---|---|---|---|---|---| | 1 | Arithmetic Sequence | 1 | 1 | 1 | 1 | 12 | | 2 | Circles | 1 | 1 | | | 6 | | 3 | Mathematics of Chance | | 1 | | | 4 | | 4 | Second Degree Eq | | | | | | | 5 | Trigonometry | 1 | 1 | 1 | 1 | 14 | | 6 | Coordinates | 1 | 2 | 2 | 2 | 26 | | 7 | Tangents | 1 | 2 | 2 | 2 | 21 | | 8 | Solids | 1 | 1 | 2 | | 13 | | 9 | Geometry and Algebra | | 1 | 1 | | 9 | | 10 | Polynomials | | | | 1 | | | 11 | Statistics | | | | | | ## Tangents **Diagrams:** 1. A circle with diameter and radii labeled. 2. A circle with a line that intersect through the circle. The point of intersection is marked as x, angle between the line and the diameter is marked as x, and the angle in the left side of x is marked as 180-x. 3. A circle with a triangle surrounded by it. The top angle of the triangle is 2x, left and right base angles are 90-x, other angles are marked as 180-2x. 4. A circle with a triangle surrounded by it. The left and right base angles of the triangle are marked as 180-x. 5. A circle with a tangent line and points A, B, and C marked. The length of side AB is a+b, side BC is b+c and side AC is a+c. 6. A circle with a triangle drawn outside it. The triangle has an altitude line, all the angles are marked: x, 2x, 180-x, and 180-2x. 7. A circle with an equilateral triangle surrounded by it. Angles are marked as follows: 60, 60, at the corner of the triangle, and 30 for every other angle. **Equations:** - *PA.PB = PC* (A and B are the points of intersection of tangents with the circle and C is the center of the circle) - *a + b + c / 2 = s* - *A = √s(s − a)(s − b)(s − c)* - *r = A / s* ## Tangent & Radius - The tangent at a point on a circle is perpendicular to the radius/diameter through that point. - The line intersecting at a point of a circle is perpendicular to the diameter of the circle. ## Tangents from an External Point - Exactly two tangents can be drawn from an exterior point to a given circle. - The lengths of these two tangents will be equal. - They will subtend equal angles at the center. ## Incircle - Centre of incircle = point of intersection of angle bisectors - *r = A / s* - *A = √s(s − a)(s − b)(s − c)* ## Constructions - Tangents ### List of Construction Problems: 1. Draw a tangent to a circle. 2. Tangent from external point (Draw a circle of x cm radius. Mark a point 7 cm away from the centre and draw 2 tangents to the circle) 3. Incircle of radius z cm with xº and yº. 4. Draw a triangle of x cm, y cm and zº and draw an incircle to it and measure the in radius. ## Diwali Offer - 25% off on all batches - Contact numbers: 75 920 920 21 & 75 920 920 22 ## SSLC LAKSHYA - Batch 2024 - 25 - Batch fee: ₹4999 ₹3999 ## Features - Learning Videos - Detailed topic-wise learning videos - Live Sessions - Doubt Clearance Live Sessions - Worksheet - Chapterwise Worksheet - Exams - Chapterwise exams, model exams, monthly combined exams - Class Notes - PDF class notes of learning videos & Live Classes - PYQ Video Solutions - Previous year question paper video solutions - One Shot - Revision one shot live classes ## SSLC LAKSHYA - Online Tuition Batch - Full syllabus recorded & live classes - Class notes in PDF format - Previous year question sessions ## Constructions **List of Construction Problems:** 1. Draw a tangent to a circle. 2. Tangent from external point (Draw a circle of x cm radius. Mark a point 7 cm away from the centre and draw 2 tangents to the circle) 3. Incircle of radius z cm with xº and yº. 4. Draw a triangle of x cm, y cm and zº and draw an incircle to it and measure the in radius. ## Model Questions 1. **MARCH 2021 (1 Mark):** - In the figure, OA is the radius of the circle. PQ is the tangent through A. What is the measure of OAP? - **Diagram:** A circle with a tangent line and points O, A, and P marked. Angle OAP marked as 90 degrees. 2. **MODEL 2019 (3 Marks):** - In the figure, C is the center of the circle, PA and PB are tangents. PC = 5 centimeters and radius of the circle is 3 centimeters. Find the length of PA and area of the quadrilateral PACB. - **Diagram:** A circle with a triangle surrounded by it. Points A, B, C, and P are marked. The length of the side PC is 5 cm, and the radius of the circle is 3 cm. 3. **MARCH 2022 (3 Marks):** - The two tangents AC and BC of the circle with center O meets at C. What is the measure of OAC? If AOB=110° find the measure of ACB. - **Diagram:** A circle with a triangle surrounded by it. Points A, B, C, and O are marked. The length of the side PC is 5 cm, and the radius of the circle is 3 cm. Angle AOB is marked as 110 degrees. 4. **MARCH 2021 (3 Marks):** - P is at a distance of 13 centimeters from the centre of a circle of radius 5 centimeters. How many tangents can be drawn from the point P to the circle? Find the lengths of the tangents. - **Diagram:** A circle with an external point P, where the distance between Point P and the circle is 13 cm, and radius of the circle is 5 cm. The length of the tangent is 12 cm. 5. **MODEL 2021 (3 Marks):** - In the figure, the circle touches the sides of the quadrilateral PQRS at A, B, C, and D. PA = 5 centimeters, QB=4 centimeters, RC = 3 centimeters, SD = 2 centimeters. What is the length of PD? Find the perimeter of the quadrilateral PQRS. - **Diagram:** A circle with a quadrilateral drawn inside it. Points P, Q, R, S, A, B , C, and D are marked. 6. **SAY 2021 (4 Marks):** - In the figure, O is the centre of the circle. PA and PB are tangents, <P = 60°. What is the measure of <AOB, <ACB, <PAB? If AB = 7 centimetres, what is the length of the tangents? - **Diagram:** A circle with a triangle surrounding it. Points A, B, C, O, and P are marked. Angle P is marked as 60 degrees. 7. **MARCH 2022 (4 Marks):** - In the figure PA=4 centimetres, AB=5 centimetres and PC is a tangent to the circle. Find the length of PC. - **Diagram:** A circle with a line segment drawn outside the circle and touches it at point C. Points A, B, C, and P are marked. The length of the side PA is 4 cm, and side AB is 5 cm. The length of the tangent is 6 cm. 8. **MODEL 2022 (8 Marks):** - a) In figure, the incircle of triangle A, B, C touches its sides at the points P, Q and R. O is the centre of the circle. Find OQB, examine whether quadrilateral POQB is cyclic, and if B = 50° then POQ = ? - b) Draw a triangle with radius of the incircle 2.5 centimetres and two angles 50°, 60°. - **Diagram:** A triangle with an incircle drawn inside. Point A, B, C, O, P, Q, and R are marked. Angles A, B, and C are marked as follows: angle A = 70, angle B = 60, and angle C = 50. 9. **MARCH 2021 (5 Marks):** - In the figure AB, BC and AC touches the circle at the points Z, X and Y. ZXY =60°, XZY = 50°. Find the measures of A, B, and C. - **Diagram:** A triangle with a circle drawn inside. Points A, B, C, X, Y, and Z are marked. Angle XZY is marked as 50 degrees and angle ZXY is marked as 60 degrees. 10. **MODEL 2021 (4 Marks):** - In the figure, the circle touches the sides of triangle ABC at P, Q and R. ∠A=70°, ∠ B=60°. What is the measure of ∠BPQ? What is ∠PRQ? Find the measures of other two angles of triangle ∠PQR. - **Diagram:** A triangle with a circle drawn inside. Points A, B, C, P, Q, and R are marked. Angle A is marked as 70 degrees and Angle B is marked as 60 degrees. 11. **MARCH 2022 (2 Marks):** - If the perimeter of a triangle is 24 centimetres and its inradius is 2 centimeters, find its area in square centimeters. 12. **MODEL 2022 (2 Marks):** - Find the radius of the incircle of a triangle with perimeter 42 centimeters and area 84 square centimetres.