Question:
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is
Updated On: Sep 30, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 24
Solution and Explanation
Refer to the below diagram
Observe that triangle BPC and BQC are inscribed inside a semicircle. Hence,
∠BPC = ∠BQC = 90°
Therefore, we can say that BQ ⊥ AC and CP ⊥ AB.
Also, In triangle ABC,
Area of triangle = (1/2)×Base×Height = (1/2)×AB×CP = (1/2)×AC×BQ
⇒ BQ = AB×CP / AC = 30×20/25 = 24 cm.
Was this answer helpful?
0
0
Top Questions on Triangles, Circles & Quadrilaterals
- A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is
- CAT - 2023
- Quantitative Aptitude
- Triangles, Circles & Quadrilaterals
- Let \(ΔABC\) be an isosceles triangle such that \(AB\) and \(AC\) are of equal length. \(AD\) is the altitude from \(A\) on \(BC\) and \(BE\) is the altitude from \(B\) on \(AC\) . If \(AD\) and \(BE\) intersect at \(O\) such that \(∠AOB =105\degree\) , then \(\frac{AD}{BE}\) equals
- CAT - 2023
- Quantitative Aptitude
- Triangles, Circles & Quadrilaterals
ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB . Kindly note that BC<AD . P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC . If the area of the triangle CPD is 4√3. Find the area of the triangle ABQ.
- XAT - 2023
- Quantitative Ability and Data Interpretation
- Triangles, Circles & Quadrilaterals
- The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.
In a cricket match, three slip fielders are positioned in a straight line. The distance between the 1st slip and the 2nd slip is the same as the distance between the 2nd slip and the 3rd slip. The player X, who is not on the same line of slip fielders, throws a ball to the 3rd slip and the ball takes 5 seconds to reach the player at the 3rd slip. If he had thrown the ball at the same speed to the 1st slip or to the 2nd slip, it would have taken 3 seconds or 4 seconds, respectively. What is the distance between the 2nd slip and player X?
1. The ball travels at a speed of 3.6 km/hour.
2. The distance between the 1st slip and the 3rd slip is 2 meters.- XAT - 2023
- Quantitative Ability and Data Interpretation
- Triangles, Circles & Quadrilaterals
- ABC is a triangle and the coordinates of A, B, and C are (a, b - 2c), (a, b + 4c), and (-2a, 3c), respectively, where a, b, and c are positive numbers. The area of the triangle ABC is:
- XAT - 2023
- Quantitative Ability and Data Interpretation
- Triangles, Circles & Quadrilaterals
View More Questions
Questions Asked in CAT exam
- For any natural Number 'n', let an be the largest number not exceeding \(\sqrt{n}\) , then a1 + a2 + a3... +a50 =
- CAT - 2024
- Number Systems
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- In September, the incomes of \(K\), \(A\), and \(V\) are in the ratio \(8:6:5\). They rent a house, contributing \(15\%\), \(12\%\), and \(18\%\) of their respective incomes. In October, the rent remains the same, but the salaries of \(K\), \(A\), and \(V\) increase by \(10\%\), \(12\%\), and \(15\%\), respectively. What percentage of their total income is paid as house rent in October? (Round to the nearest percentage.)
- CAT - 2024
- Percentages
View More Questions