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Standard X

Mathematics

No. of Tangents to a Circle from a Given Point

Directions: I...

Question

Directions: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).
Mark the correct choice as:
Assertion (A): If in a circle, the radius of the circle is 3 cm and the distance of a point from the centre of a circle is 5 cm, then length of the tangent will be 4 cm.
Reason (R): (Hypotenuse)² = (Base)² + (Height)²

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

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Assertion (A) is true, but Reason (R) is false.

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Assertion (A) is false, but Reason (R) is true.

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Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

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Solution

The correct option is D Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A)

(OA)² = (AB)² + (OB)²
AB = $\sqrt{25 - 9}$ = 4 cm

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Similar questions

Q. Direction: In the following question, a statement of assertion (A) is followed by a statement of reason (R).
Mark the correct choice as:

Assertion: In a circle of radius 6cm, the angle of sector is 60°. The area of the sector is $18 \frac{6}{7} c m^{2}$ .

Reason: The circumference of a circle with radius $r$ is $2 π r$ .

Q. Assertion :If in a circle, the radius of the circle is

3 c m

and distance of a point from the centre of a circle is

5 c m

, then length of the tangent from that point will be

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. Reason:

(hypotenuse)^{2} = (base)^{2} + (height)^{2}

Q. Directions: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).
Mark the correct choice as:

Assertion (A): D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC then the value of

a

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a

cm, DB =

(a - 4)

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cm and EC =

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Q. Direction: In the following question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion: In the given figure, ∠BAO = 30° and ∠BCO = 40°, then the measure of ∠AOC = 60°.

Reason: The angle subtended by an arc of a circle at the centre of the circle is twice the angle subtended by that arc on the remaining part of the circle.

Q. In the following question, a statement of assertion (A) is followed by a statement of reason (R).

Mark the correct choice as:

Assertion: In a circle of radius 6 cm, the angle of sector is $60 °$ . Then area of sector is $18 \frac{6}{7} c m^{2}$ .

Reason: The circumference of a circle with radius 𝒓 is 𝟐𝝅𝒓.

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The correct option is D Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A) (OA)2 = (AB)2 + (OB)2 AB = √25−9 = 4 cm

The correct option is D Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A)

(OA)² = (AB)² + (OB)²
AB = $\sqrt{25 - 9}$ = 4 cm