Ask Experts Questions for FREE Help !
Ask
    sangam007's Avatar
    sangam007 Posts: 4, Reputation: 1
    New Member
    		  
    #1

    Feb 6, 2011, 12:34 AM
    Isosceles triangle area
    If an isosceles triangle ABC in which AB=AC=6cm is inscribed in a circle of radius 9cm.Find the area of triangle ABC.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
    		  
    #2

    Feb 6, 2011, 04:41 AM

    Make a sketch, and join the vertices of the isosceles triangle to the centre of the circle. You'll notice that you now have 3 triangles, two of which are similar and one other triangle.

    You can find the angles AOC, AOB and BOC, where O is the centre of the triangle, making use of the cosine rule. Once you get the angles, you can find the area using the formula:
    ptjain's Avatar
    ptjain Posts: 2, Reputation: 2
    New Member
    		  
    #3

    Feb 23, 2011, 09:32 AM
    The given information can be represented using a figure as:


    Let AM = x cm
    In quadrilateral OBAC, OB = OC = 9 cm and AB = AC = 6 cm
    Thus, OBAC is a kite. It is known that the diagonals of a kite are perpendicular to each other.
    ∴ OA ⊥ BC
    In right angled ∆AMC,
    AM2 + MC2 = AC2 [Pythagoras theorem]
    â‡' MC2 = (62 – x 2) cm2

    Using Pythagoras theorem for ∆OMC, it is obtained
    OM2 + MC2 = OC2
    â‡' (9 – x)2 + (62 – x 2) = 92
    â‡' 81 + x 2 – 18x + 36 – x 2 = 81
    â‡'18x = 36
    â‡'x = 2
Not your question? Ask your question View similar questions
 

Question Tools Search this Question
Search this Question:

Advanced Search

Add your answer here.


Check out some similar questions!

Perimeter of an Isosceles Triangle [ 16 Answers ]

What is the hypotenuse of an isosceles triangle if the perimeter is 16 + 16 radical 2?

Area of isosceles triangle given circle radii [ 8 Answers ]

Here is a fun little geometry problem. Give it a go if you so desire. Look at the graph. The radius of the larger circle is 2r and the radius of the smaller circle is r. Find the area of the triangle. There are many ways to go about it. I used simialr triangles, but perhaps you have a better...

Isosceles triangle [ 3 Answers ]

Find the perimeter of an isosceles triangle if the vertex angle measures 50 degrees and the length of the base is 28 cm. help.tnx

Isosceles triangle [ 2 Answers ]

The area of an isosceles triangle is 30 square units.if the base measure 6 units,find the length of the altitude and the ratio of the altitude to the base?

Isosceles triangle [ 1 Answers ]

the sum of the square roots of any two sides of an isoseles triangle is equal to the square root of the remaining side. Is this statement true or false?

View more questions Search