If U, V are the centres of the circles M and N respectively, then what is the area of the quadrilateral formed by the points P, Q, V and U?
Consider the following for the next two (02) items that follow :<br>A circle M of radius 8 cm touches externally with another circle N of radius 16 cm. Let P, Q be the points where the common tangent touches the circles M and N respectively.
- A. 192\sqrt{2} square cm ✓
- B. 192 square cm
- C. 96\sqrt{2} square cm
- D. 96 square cm
Correct Answer: A. 192\sqrt{2} square cm
Explanation
Quadrilateral UPQV is a right trapezium with parallel sides UP = 8 cm and VQ = 16 cm, and height PQ = 16\sqrt{2} cm. Area = \frac{1}{2}(UP+VQ)\times PQ = \frac{1}{2}(8+16)\times 16\sqrt{2} = 12 \times 16\sqrt{2} = 192\sqrt{2} sq cm.
Related questions on Mensuration
- A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
- A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
- A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
- A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
- Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...