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Class 10 Maths Chapter 10 Circles
Given: A circle with center O and radius r. Let P be a point on the circle where a tangent TP is drawn. To Prove:The tangent TP is perpendicular to the radius OP, i.e., Proof: Consider a circle with center O and a tangent TP at point P.Since P lies on the circle, OP is the radius of the circle. AssuRead more
Given: A circle with center O and radius r. Let P be a point on the circle where a tangent TP is drawn.
To Prove:The tangent TP is perpendicular to the radius OP, i.e.,
Proof: Consider a circle with center O and a tangent TP at point P.Since P lies on the circle, OP is the radius of the circle.
Assume another point Q on the tangent TP (other than P).Since Q lies outside the circle, the line segment OQ is longer than OP (as OP is the shortest distance from O to the circle).
In any circle, a line drawn from the center to a point outside the circle is always longer than the radius.That means:for all points Q on the tangent other than P.
This implies that OP is the shortest distance from O to the tangent.By the definition of perpendicularity, the shortest distance from a point to a line is along the perpendicular.
Thus, OP must be perpendicular to TP.
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Name the right which is known as the heart and soul of Indian Constitution.
Correct Answer: (b) Right to Constitutional Remedies Explanation: Dr. B.R. Ambedkar referred to the Right to Constitutional Remedies as the "heart and soul" of the Indian Constitution because: It allows citizens to approach the Supreme Court or High Courts if their fundamental rights are violated. IRead more
Correct Answer: (b) Right to Constitutional Remedies
Explanation: Dr. B.R. Ambedkar referred to the Right to Constitutional Remedies as the “heart and soul” of the Indian Constitution because: It allows citizens to approach the Supreme Court or High Courts if their fundamental rights are violated. It empowers the courts to issue writs like Habeas Corpus, Mandamus, Prohibition, Certiorari, and Quo Warranto to protect citizens’ rights. It acts as a safeguard for all other Fundamental Rights (Articles 12-35). This right is enshrined in Article 32 of the Indian Constitution and is considered essential for the protection of democracy and individual freedoms in India. This question related to Chapter 5 Social Science Class 9th NCERT. From the Chapter 5 Democratic Rights. Give answer according to your understanding.
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If 18, a, b, -3 are in A.P., the a + b =
Given terms in A.P.: 18, a, b, -3 We'll find the common difference (d): Since we have 4 terms, and first & last terms are given: 18 + d = a (1st equation) a + d = b (2nd equation) b + d = -3 (3rd equation) Total difference from first to last term = 3d Thus: 18 - (-3) = 3d 21 = 3d d = -7 Now, putRead more
Given terms in A.P.: 18, a, b, -3
We’ll find the common difference (d):
Since we have 4 terms, and first & last terms are given:
18 + d = a (1st equation)
a + d = b (2nd equation)
b + d = -3 (3rd equation)
Total difference from first to last term = 3d
Thus:
18 – (-3) = 3d
21 = 3d
d = -7
Now, putting d = -7 in equations:
From 1st equation:
18 + (-7) = a
a = 11
From 2nd equation:
11 + (-7) = b
b = 4
Thus: a + b = 11 + 4 = 15
See lessHow safety of women has been ensured through Fundamental Rights?
Correct Answer: (c) Prohibition of traffic in human beings Explanation: The safety and dignity of women have been ensured through Article 23 of the Indian Constitution, which prohibits: Human trafficking and forced labor – This prevents women from being exploited in illegal activities like prostitutRead more
Correct Answer: (c) Prohibition of traffic in human beings
Explanation: The safety and dignity of women have been ensured through Article 23 of the Indian Constitution, which prohibits: Human trafficking and forced labor – This prevents women from being exploited in illegal activities like prostitution, bonded labor, and slavery. Exploitation in any form – It ensures that no woman is forced into any form of servitude or unfair treatment. Legal protection – The government has enacted laws like The Immoral Traffic (Prevention) Act, 1956, and The Protection of Women from Domestic Violence Act, 2005, to further strengthen women’s safety.
Apart from Article 23, Right to Equality (Article 14-18) and Right to Life & Personal Liberty (Article 21) also play a crucial role in ensuring women’s protection and empowerment in India.
This question related to Chapter 5 Social Science Class 9th NCERT. From the Chapter 5 Democratic Rights. Give answer according to your understanding.
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If 5 times the 5ᵗʰ term of an AP is equal to 8 times the 8ᵗʰ term then find its 13ᵗʰ term
Given: 5a₅ = 8a₈ where aₙ = a₁ + (n-1)d Let's substitute terms: 5[a₁ + 4d] = 8[a₁ + 7d] 5a₁ + 20d = 8a₁ + 56d 5a₁ - 8a₁ = 56d - 20d -3a₁ = 36d a₁ = -12d Now, for 13th term: a₁₃ = a₁ + 12d = -12d + 12d = 0 Thus, the 13th term of this AP is 0. Click here for more: https://www.tiwariacademy.in/ncert-soRead more
Given: 5a₅ = 8a₈
where aₙ = a₁ + (n-1)d
Let’s substitute terms:
5[a₁ + 4d] = 8[a₁ + 7d]
5a₁ + 20d = 8a₁ + 56d
5a₁ – 8a₁ = 56d – 20d
-3a₁ = 36d
a₁ = -12d
Now, for 13th term:
a₁₃ = a₁ + 12d
= -12d + 12d
= 0
Thus, the 13th term of this AP is 0.
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