NCERT Solutions Class 10 Maths Chapter 10 — Circles

Solution:

Step 1: A tangent is defined as a line that intersects the circle at exactly one point. This point is called the point of contact.

Step 2: Options A describes a secant, option B describes a line containing a diameter, and option D describes a chord.

Solution:

Step 1: If a point P lies inside a circle, any line passing through P will necessarily intersect the circle at two distinct points.

Step 2: By the definition of a tangent (touching at exactly one point), no tangent can be drawn to the circle from a point lying inside it.

Solution:

Step 1: According to Theorem 1, the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Step 2: Therefore, the radius OP is perpendicular to the tangent PQ at point P.

Step 3: This means ∠OPQ = 90°.

Solution:

Step 1: Theorem 1 states that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Step 2: Perpendicular lines form an angle of 90°.

Step 3: Therefore, ∠OPA must be 90°, not 60°.

Solution:

Step 1: Option A is false; a tangent does not pass through the center. Option C is false; a tangent intersects at exactly one point. Option D is false; there is no such general rule for the length of a tangent.

Step 2: Theorem 1 states that the radius drawn to the point of contact is perpendicular to the tangent. This statement is correct.