Question
In a circle, two tangents PA and PB are drawn from an
external point P such that the angle ∠APB = 60°. If the radius of the circle is 10 cm, find the length of each tangent.Solution
In a circle, the tangents drawn from an external point are equal in length. Let the length of the tangent be x cm. In triangle ∆APB, since PA = PB, ∆APB is an isosceles triangle. Also, ∠APB = 60°. Using the cosine rule: x² = 10² + 10² − 2(10)(10)cos(60°) x² = 100 + 100 − 200 × (1/2) x² = 200 − 100 x² = 100 x = 10 cm Correct answer: a) 10 cm
The heights (in cm) of 9 basketball players in a tournament are as follows: 178, 182, 175, 180, 184, 179, 177, 181, 183
Find the median height of...
- Three years ago, age of A was 10 years less than 1.2 times his current age. The ratio of age of B, 3 years later to the age of C, 1 year ago is 3:2. Find t...
- Karan is 4 years older than Tarun, and Tarun is 6 years younger than Naman. If 3 years later, the ratio of Karan’s age to Naman’s age will be 7:8, find...
A is younger than B by 4 years. If the ratio of A and B ages is 5:7 respectively, then find the age of A.
The present ages of Amit and Sumit are in the ratio of 5:3, respectively. After 6 years from now, if the difference between the age of Amit and Sumit wi...
- The ratio of the ages of two friends is 4:3, respectively. If the difference between their ages is 9 years, then find the age of the younger friend.
If the total ages of A and B is 10 years more than the total age of B and C. C is how many years younger than A?
The ratio of A's age to B's age after 18 years will be 5:6. Seven years ago, the ratio of their ages was 5:7. Find the present average age of A and B.
The current ages of A and B have a ratio of 7:9. Twelve years from now, B will be 12 years older than A. What will be the ratio of their ages in six years?
A’s age is 120% of what he was 4 years ago, But 30% of what it will be after 5 years. What is his present age?
