Thread: Help me out these easy geometry problems.?

I want the explanation too, cause i don't understand the question properly and then put it clearly, cause i am just 8th class student. best of answers will be given 5 *'s, plus a thumbs up.

1.In ▲ PQR, PD ┴ QR and PO is the bisector of ∠ QPR. If ∠ PQR = 65° and ∠ PQR = 23.5°,then
∠ DPO in degrees=
2.In a parallelogram PQRS,the bisectors of ∠ P and ∠ Q meet on RS.If the perimeter PQRS is 13.5 cm, then the measure of QR =
3.A circle is passing through three vertices of a rhombus of side 8cm and its centre is the forth vertex of the rhombus. Find the length of the longest diagonal of the rhombus.
4.In a rhombus ABCD, the diagonals intersect each other at O.If ∠ A = 60° and OA = 2 cm, then the side of the rhombus is =
5.In a rhombus PQRS,the diagonals intersect at O.Given that, ∠ P = 120° and OP = 3 cm. What is the side of the rhombus is =
6.P is an interior point of quadrilateral ABCD and B = 3.5 cm,BC = 4 cm,CD = 4.8 cm and AD = 3.7 cm.Then the possible value of ( AP+BP+CP+DP) =
7. MN and PS are 2 equal chords of a circle drawn on the either side of centre O of the circle. Both the chords are produced to meet at point A.If the radius of the circle is 10 cm, MN = 12 cm and OA= 17 cm, then NA =
8. In ▲ ABC , if ∠ A < ∠ B < 45°, then ▲ ABC is a/an .................................... triangle.
9. If G is the centroid of ▲ ABC, then the area of ▲ BGC is ............................... thimes the area of the quadrilateral ABCG.

If you can provide a diagram also, it is good.... but if you can't it's not even a silly problem.. Please answer this question.I am trying for many Days ( nearly about 4 days.) Help me out.. ♣♣

Hello, kohila!

Here is some help . . .

3. A circle is passing through three vertices of a rhombus of side 8cm
and its centre is the forth vertex of the rhombus.
Find the length of the longest diagonal of the rhombus.

We have rhombus .
The center of the circle is
Since , the rhombus
. . is made of two equilateral triangles.
Hence:

Code:

                  B
                  *
           8   *  :  *   8
            *     :     *
         *        :        *
    A *  *  *  *  *  *  *  *  * C
         *        :        *
            *     :     *
           8   *  :  *   8
                  *
                  O

Law of Cosines: .

. . . . . . . . . . . .

Therefore: .

4. In a rhombus ABCD, the diagonals intersect each other at O.
If ∠ A = 60° and OA = 2 cm, find the length of a side of the rhombus.

Once again, the rhombus is comprised of two equilateral triangles.

Code:

                  B
                  *
               *  :  *
            *     :     *
         *    2   :        *
    A *  -  -  -  +  -  -  -  * C
         *        :O       *
            *     :     *
           8   *  :  *   8
                  *
                  D

The altitude of the equilateral triangle is 2.

Code:

            *
           *|*
          * | * x
         *  |2 *
        *   |   *
       *    |    *
      * * * * * * *
              x/2

Pythagorus: .

. . . . . . . . .

. . . . . . . . . .

thank you.. you can answer all but y u delayed.