Question:medium
Consider a right-angled triangle ABC, right angled at B. Two circles, each of radius r, are drawn inside the triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The two circles also touch each other (see the image below).
If AB = 18 cm and BC = 24 cm, then find the value of r.
![If AB = 18 cm and BC = 24 cm, then find the value of r.]()
Consider a right-angled triangle ABC, right angled at B. Two circles, each of radius r, are drawn inside the triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The two circles also touch each other (see the image below).
If AB = 18 cm and BC = 24 cm, then find the value of r.
![If AB = 18 cm and BC = 24 cm, then find the value of r.]()
If AB = 18 cm and BC = 24 cm, then find the value of r.
Updated On: Nov 26, 2025
- 3 cm
- 4 cm
- 3.5 cm
- 4.5 cm
- None of the remaining options is correct.
Top Questions on Geometry
- A solid trophy, consisting of two parts, has been designed in the following manner: the bottom part is a frustum of a cone with the bottom radius 30 cm, the top radius 20 cm, and height 40 cm, while the top part is a hemisphere with radius 20 cm. Moreover, the flat surface of the hemisphere is the same as the top surface of the frustum. If the entire trophy is to be gold-plated at the cost of Rs. 40 per square cm, what would the cost for gold-plating be closest to?
- A straight line \( L_1 \) has the equation \( y = k(x - 1) \), where \( k \) is some real number. The straight line \( L_1 \) intersects another straight line \( L_2 \) at the point (5, 8). If \( L_2 \) has a slope of 1, which of the following is definitely FALSE?
- ABCD is a rectangle, where the coordinates of C and D are (-2,0) and (2,0), respectively. If the area of the rectangle is 24, which of the following is a possible equation representing the line AB?
- ABCD is a rectangle where points C and D have coordinates (−2, 0) and (2, 0), respectively. If the area of the rectangle is 24, what is the best way to describe the equation of the line AB?
- Want to practice more? Try solving extra ecology questions todayView All Questions