Circles:
The chapter 'Circles' carrying the weightage of 6 - 7 marks in the board examination. It covers the concepts like tangent to a circle, length of tangent from a point, tangent from an external point.
Most possible variation of question types that we can expect in board exam as per previous year question paper are discussed below.
| Total marks 6 - 7 | |
| Variation 1 | Variation 2 |
Total marks=6
|
Total marks=7
|
To prepare well for the board examination, it is necesary to understand the following concepts clearly.
- Tangent to a circle - Length of a tangent, one tangent form, radius perpendicualr to tangent at point of contact.
- Number of tangents
- Tangent from an external point.
| Important Concept (Learning Outcomes) | Expected Question Type | Concept deat with |
| Tangent to a circle | Sec A, Sec B, Sec, Sec C | |
| Tangent to a circle | Sec D | |
| Tangent from an external point | Sec A, Sec B, Sec C, Sec D |
Let us recall the concepts in circles:
Tangent: The tangent to a circle is perpendicular to the radius through the point of contact.
Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact
Theorem 2: The length of the tangents drawn from an exterior point to a circle are equal.
Common mistakes to avoid:
1. Placing the \(90^\circ\) at the wrong place: The \(90^\circ\) angle is always at the point of contact between the radius and tangent.
2. Tangents are equal only when they are drawn from the same external point.
3. Confusing the angles between tangents and at the centre
For two tangents: \(\angle PTQ + \angle POQ = 180^\circ\)
They are supplementary, not equal.
4. Radius is perpendiuclar to the tangent at the point of contact.
5. Clealry mark the point of contact, right angle, centre and tangent. Ensure the tangent touches the circle at only one point.
Exam tips & tricks:
1. For every circles question, run this quick mental checklist:
2. If there is a tangent, draw radius to the point of contact, mark \(90^\circ\)
3. If there an external point with two tangents, mark those two tangent segments equal.
4. If there a quadrilateral with tangets, use sum of opposite sides are equal type results from tangent lenghts.
5. If there is a right angle triangle formed, apply pythagoras with correct hypotenuse.