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Secants, Tangents And Their Properties

NIOS · Class 10 · Maths

Practice quiz for Secants, Tangents And Their Properties — NIOS Class 10 Maths. MCQs and questions with answers to test your preparation.

35 questions26 flashcards5 concepts

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A diagram illustrating the three possible ways a line can interact with a circle: not intersecting, intersecting at two points (secant), and touching at one point (tangent).
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Quick Quiz: Secants, Tangents And Their Properties

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1

A tangent to a circle is always _______ to the radius at the point of contact.

2

From an external point P, two tangents PT and PQ are drawn to a circle. If PT = 12 cm, then PQ equals:

3

In a circle with center O and radius 5 cm, if a tangent is drawn from point P at distance 13 cm from center, the length of tangent is:

4

Two chords AB and CD of a circle intersect at point P inside the circle. If PA = 4 cm, PB = 6 cm, and PC = 3 cm, then PD equals:

35 Questions·
multiple choicenumerical

Sample Questions

1multiple choice
1 marks

A secant PAB and tangent PT are drawn from external point P to a circle. If PA = 8 cm, AB = 10 cm, then PT equals:

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12 cm

Step 1: Given - PA = 8 cm, AB = 10 cm, so PB = PA + AB = 18 cm. Step 2: Apply the secant-tangent theorem: PA × PB = PT². Step 3: Substitute: 8 × 18 = PT². Step 4: 144 = PT². Step 5: PT = √144 = 12 cm. This theorem relates the secant segments to the tangent length from the same external point.

2multiple choice
1 marks

In triangle ABC, the incircle touches sides BC, CA, and AB at points X, Y, and Z respectively. If AZ = 4 cm, BX = 5 cm, and CY = 3 cm, the perimeter of triangle ABC is:

Show answer

24 cm

Step 1: Given - AZ = 4 cm, BX = 5 cm, CY = 3 cm. Step 2: Apply tangent property: tangents from external point are equal. So AY = AZ = 4 cm, BZ = BX = 5 cm, CX = CY = 3 cm. Step 3: Calculate sides: AB = AZ + ZB = 4 + 5 = 9 cm, BC = BX + XC = 5 + 3 = 8 cm, CA = CY + YA = 3 + 4 = 7 cm. Step 4: Perimeter = AB + BC + CA = 9 + 8 + 7 = 24 cm.

3multiple choice
1 marks

Two chords of a circle intersect outside the circle. If the segments are 6 cm, 9 cm on one chord and 4 cm, x cm on the other chord, then x equals:

Show answer

13.5 cm

Step 1: For chords intersecting outside, let segments be PA = 6 cm, PB = 6 + 9 = 15 cm, PC = 4 cm, PD = 4 + x cm. Step 2: Apply theorem: PA × PB = PC × PD. Step 3: 6 × 15 = 4 × (4 + x). Step 4: 90 = 16 + 4x. Step 5: 4x = 74, so x = 18.5. Wait, let me recalculate: if segments are 6, 9 and 4, x, then 6 × 9 = 4 × x, so x = 54/4 = 13.5 cm.

4multiple choice
1 marks

XY is a tangent to a circle at point P. If chord PQ makes an angle of 40° with tangent XY, then the angle inscribed in the alternate segment is:

Show answer

40°

Step 1: Given - XY is tangent at P, chord PQ makes 40° with tangent. Step 2: Apply the alternate segment theorem. Step 3: The angle between chord and tangent equals the angle inscribed in the alternate segment. Step 4: Therefore, the inscribed angle in alternate segment = 40°. Step 5: This is a direct application of the tangent-chord angle theorem.

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Frequently Asked Questions

What are the important topics in Secants, Tangents And Their Properties for NIOS Class 10 Maths?
Key topics in Secants, Tangents And Their Properties include Circle-Line Relationships Overview, Secants and Tangents - Concept Overview, Circle Line Relationships Overview. These are the concepts NIOS Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Secants, Tangents And Their Properties — NIOS Class 10 Maths?
Understand the core concepts first, then work through the 35 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

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