Question
Two circles with centers B and D have radii DA = 8 cm
and BC = x cm, respectively. AC is tangent to both circles. If DB and AC intersect the point E, AE = 12 cm, and EC = 18 cm, then find the value of x (in cm).Solution
AD ⊥ AC and BC ⊥ AC ∠DAE = ∠BCE = 90° In △ DAE and △ BCE ∠DAE = ∠BCE = 90° ∠AED = ∠BEC (Vertical angle) △ DAE ~ △ BCE (By AA similarity) By C.P.C.T = AE/EC = AD/BC = 12/18 = 8/BC  BC = (18×8)/12 =144/12 x= 12cm  The correct answer is 12 cm.
A rectangular playground is fenced at Rs. 11/metre and the total cost is Rs. 1210. If the length to breadth ratio is 6:5, find the area of the playground.
In an equilateral triangle ABC, D is the midpoint of side BC. If the length of BC is 8 cm, then the height of the triangle is:
A candidate just passed by getting 150 answers correct by attempting 225 of the total questions. Find the total number of questions in the examination i...
A metallic sphere of radius 4.2 cms. Is melted and recast into the shape of a cylinder of radius 6 cms. Height of the resultant cylinder would be:
If the total surface area of a cube is 486 cm², then calculate the volume of the cube.
A cone is parallel to its base in such a way that the volume of the smaller cone is  1/2197 times of the bigger cone. Find the height of the smaller co...
A cuboidal box with dimensions 12.5 cm (length), 7.5 cm (breadth), and 10 cm (height) is open from the top. The box is to be painted from the outside. I...
A conical tent of height 5m and base diameter 24m was erected by a company in a park. Find the curved surface area of the tent (in m²).
The volume of a cube is given as 8×(x+3)3 m3. The length of a rectangle is twice the side length of the cu...
If the volume of a cylinder is 486Ï€ and the ratio of radius to its height is 3:2 then find the curved surface area of cylinder?
Relevant for Exams:
