Question
The length of a tangent from a point A at a distance 5
cms. from the centre of the circle is 4 cms. Radius of the circle isSolution
A tangent at any point of a circle is perpendicular to the radius through the point of contact. Therefore, ∠OTA = 90° and ΔOTA is a right-angled triangle. By Pythagoras theorem, OA2 = OT2 + AT2 52 = OT2 + 42 OT2 = 25 - 16 OT2 = 9 OT = ± 3 Radius OT cannot be negative. Hence, the radius is 3 cm.
- Neha spent 30% of her income on education and out of the remaining amount, she spent 25% on travel, 20% on health, 15% on entertainment, and saved Rs. 2000...
- The value of a piece of land increases by 12% each year. If the present value is ₹1,50,000, find the value after 2 years.
Sahil spent 10% of his monthly income on education, 20% on entertainment, 15% on rent, 40% on travelling and the rest on food. If the difference between...
Rahul spends 80% of his salary and earns an allowance of 5% of his salary each month. His annual saving is Rs. 94500. Find his monthly allowance.
...The ratio of income and expenditure of a man is 6 : 5, respectively. If the income and expenditure of the man are increased by 25% and 10% respectively...
Income of 'A' is Rs. 1,800 more than that of 'B'. Both spend 25% of their respective incomes. If the savings of 'C' is 18.75% of his income and is equa...
Raman spends 15% of his income on house rent, 20% of the remaining on food, 25% of the now remaining on education, (3/17)th of the now remaining on trav...
A number is initially increased by 24% and subsequently reduced by 30%. Determine the overall percentage change in the number, indicating whether it is ...
Out of 1200 people in a city, 40% speak Mandarin and the rest speak Cantonese. If out of non-Mandarin speakers, 35% are males and out of Mandarin speake...
Monthly income of A is Rs. 7000 and he saves 28% of his monthly income. If monthly expenditure of A is decreased by 35% while his monthly savings is inc...
Relevant for Exams:
