class 10th maths chapter 10 notes

Important full class 10th maths chapter 10 notes of Tangent to a circle of Mathematics 10th class by Dear Respectable Sir M. Ramzan Suib. These handwritten and Composed notes are very helpful in the preparation of class 10th maths chapter 10 notes for students of the 10th class Mathematics and these are according to the paper patterns of all Punjab boards.

• Important class 10 maths chapter 10 notes for all students of Punjab  Textbook Board.
• Important MCQs of Chapter No.10: Tangent to a circle of Mathematics 10th class.
• Important definitions of Chapter No.10: Tangent to a circle of Mathematics 10th class.
• Solutions of Chapter No.10: Tangent to a circle of Mathematics 10th class.
• Important problems of Chapter No.10: Tangent to a circle of Mathematics 10th class.
• Multiple Choice Questions. Four possible answers are given for the following questions. Tick the correct answer.
• (i) In the adjacent figure of the circle, the line PTQ is named as:  (a) an arc  (b) a chord  (c) a tangent  (d) a secant
• (ii) In a circle with centre O, if OT is the radial segment and PTQ is the tangent line, then:  (a) OT ⊥ PQ  (b) OT ≠ PQ  (c) OT ∥ PO  (d) OT is right bisector of PQ
• (iii) In the adjacent figure, find semicircular area if π = 3.1416 and mOA = 20cm.  (a) 62.83sq cm  (b) 314.16sq cm  (c) 436.20sq cm  (d) 628.32sq cm
• (iv) In the adjacent figure. find half the perimeter of circle with centre O if π = 3.1416 and mOA = 20cm:  (a) 31.42 cm  (b) 62.832 cm  (c) 125.65 cm  (d) 188.50 cm
• (v) A line which has two points in common with a circle is called:  (a) sine of a circle  (c) tangent of a circle  (b) cosine of a circle  (d) secant of a circle
• (vi) A line which has only one point in common with a circle is called:  (a) sine of a circle  (b) cosine of a circle  (c) tangent of a circle  (d) secant of a circle
• Prove the following theorems alongwith corollaries and apply them to solve appropriate problems.
• If a line is drawn perpendicular to a radial segment of a circle at its outer end point, it is tangent to the circle at that point.
• The tangent to a circle and the radial segment joining the point of contact and the centre are perpendicular to each other.
• The two tangents drawn to a circle from a point outside it, are equal in length.
• If two circles touch externally or internally, the distance between their centres is respectively equal to the sum or difference of their radii.
• Two circles with radii 5cm and 4cm touch each other externally. Draw another circle with radius 2.5cm touching the first pair, externally.
• If the distance between the centres of two circles is the sum or the difference of their radii they will touch each other.
• Important definitions of Chapter No.10: Tangent to a circle:
• A secant is a straight line which cuts the circumference of a circle in two distinct points. In the figure, the secant CD cuts the circle at two distinct points P and Q.
• A tangent to a circle is the straight line which touches the circumference at one point only. The point of tangency is also known as the point of contact in the figure. AB is the tangent line to the circle at the point T.
• The length of a tangent to a circle is measured from the given point to the point of contact.
• If a line is drawn perpendicular to a radial segment of a circle at its outer end point, it is tangent to the circle at that point.
• The tangent to a circle and the radial segment joining the point of contact and the centre are perpendicular to each other.
• The two tangents drawn to a circle from a point outside it, are equal in length.
• If two circles touch externally or internally, the distance between their centres is respectively equal to the sum or difference of their radii.