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If angle between two radii of a circle is 130°, the angle between the tangents at the ends of radii is
We are given: - The angle between two radii of a circle is 130°. Key property of tangents The tangents at the ends of the two radii are perpendicular to their respective radii. Therefore, the angle between the tangents is the **supplement** of the angle between the radii. Calculate the angle betweenRead more
We are given:
– The angle between two radii of a circle is 130°.
Key property of tangents
The tangents at the ends of the two radii are perpendicular to their respective radii. Therefore, the angle between the tangents is the **supplement** of the angle between the radii.
Calculate the angle between the tangents
The sum of the angle between the radii and the angle between the tangents is 180°. Thus:
Angle between tangents = 180° – Angle between radii.
Substitute the given angle between the radii:
Angle between tangents = 180° – 130° = 50°.
This question related to Chapter 10 Mathematics Class 10th NCERT. From the Chapter 10 Circle. Give answer according to your understanding.
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The maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is
When two circles intersect at two distinct points, the maximum number of common tangents that can be drawn is 2. These tangents are the **external tangents**, as the circles are close enough to each other and intersect, so no internal tangents can exist. Explanation: - If two circles intersect at twRead more
When two circles intersect at two distinct points, the maximum number of common tangents that can be drawn is 2. These tangents are the **external tangents**, as the circles are close enough to each other and intersect, so no internal tangents can exist.
Explanation:
– If two circles intersect at two points, they share a region of overlap.
– Only two external tangents can be drawn, one on each side of the circles.
– No internal tangents are possible because the circles are not separate or disjoint.
This question is connected to Chapter 10 of the Class 10th NCERT Mathematics textbook, which focuses on “Circles.” Provide your response based on your comprehension of the concepts discussed in this chapter.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If from a point A which is at distance of 13 cm from the centre O of a circle of radius 5cm, the pair of tangent AB and AC to the circle are drawn, then the area of quadrilateral ABOC is
Given: - OA = 13 cm, OB = OC = 5 cm (radius), - Tangent length AB = AC = √(OA² - OB²) = √(13² - 5²) = 12 cm. Area of ΔABO = (1/2) × AB × OB = (1/2) × 12 × 5 = 30 cm². Similarly, Area of ΔACO = 30 cm². Total area of ABOC = 30 + 30 = 60 cm². This question pertains to Chapter 10 of the Class 10th NCERTRead more
Given:
– OA = 13 cm, OB = OC = 5 cm (radius),
– Tangent length AB = AC = √(OA² – OB²) = √(13² – 5²) = 12 cm.
Area of ΔABO = (1/2) × AB × OB = (1/2) × 12 × 5 = 30 cm².
Similarly, Area of ΔACO = 30 cm².
Total area of ABOC = 30 + 30 = 60 cm².
This question pertains to Chapter 10 of the Class 10th NCERT Mathematics textbook, specifically the chapter on “Circles.” Provide your answer in accordance with the knowledge and understanding you have gained from studying this chapter.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If two perpendicular tangents PA and PB are drawn from an external point to a circle of radius 4cm, then the length of each tangent is
Given: - Radius of circle = 4 cm, - Tangents PA and PB are perpendicular. The tangents form a square with the radii. The diagonal of the square is the hypotenuse: Diagonal = √(4² + 4²) = √32 = 4√2. Side (tangent length) = Diagonal / √2 = 4√2 / √2 = 4 cm. This question is associated with Chapter 10 oRead more
Given:
– Radius of circle = 4 cm,
– Tangents PA and PB are perpendicular.
The tangents form a square with the radii. The diagonal of the square is the hypotenuse:
Diagonal = √(4² + 4²) = √32 = 4√2.
Side (tangent length) = Diagonal / √2 = 4√2 / √2 = 4 cm.
This question is associated with Chapter 10 of the Class 10th NCERT Mathematics textbook, which deals with the topic of “Circles.” Answer the question based on your understanding of the concepts covered in this chapter.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If PA and PB are tangents to the circle with the centre O such that angle APB = 50°, then angle OAB is equal to
We are given: - PA and PB are tangents to the circle with center O, - Angle ∠APB = 50°. Key property of tangents The tangents PA and PB are equally inclined to the line joining the external point P to the center O. Therefore: ∠APO = ∠BPO = ∠APB / 2. Substitute ∠APB = 50°: ∠APO = ∠BPO = 50° / 2 = 25°Read more
We are given:
– PA and PB are tangents to the circle with center O,
– Angle ∠APB = 50°.
Key property of tangents
The tangents PA and PB are equally inclined to the line joining the external point P to the center O. Therefore:
∠APO = ∠BPO = ∠APB / 2.
Substitute ∠APB = 50°:
∠APO = ∠BPO = 50° / 2 = 25°.
Relationship between angles
In triangle OAB:
– OA and OB are radii of the circle, so triangle OAB is isosceles.
– The angle ∠OAB is equal to ∠APO because the tangent PA is perpendicular to the radius OA.
Thus:
∠OAB = ∠APO = 25°.
This question is linked to Chapter 10 of the Class 10th NCERT Mathematics textbook, which is on the topic of “Circles.” Respond with an answer that reflects your understanding of the chapter.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/