## Important Examples

**Example1:**ABCD is a cyclic quadrilateral. AB and CD are produced to meet P. If angleADC = `70^o` and angle DAB = `60^o`, then what will be angle PBC + angle PCB?

**Solution:**First step: Make an appropriate figure using statements provided in questions.

- Cyclic quadrilateral has all its vertices on circle and sum of all angles is `360^o`.
- Sum of opposite angles = `180^o`.
- External angle = Opposite internal angle.

`angle` PCB = `60^o`

So, PBC + PCB = `130^0`

See its very simple question, if you know the properties of geometry.Lets try more examples

**Example2:**ABCD is a parallelogram and P is any point within it. If area of parallelogram is 20 units, then what will be the sum of areas of triangle PAB and PCD?

**Solution:**According to the question, figure will be as follows:

Properties for this question:

- Area of parallelogram = Base `times` Height.
- Area of triangle = `1/2` Base `times` altitude.

i.e. Base `times` Height = 20

⇒ b `times` h = 20

To find = Area of ( PAB +PCD)

⇒ `(1/2) b times (PY)` + `(1/2) b times (PX)` ( See Figure)

⇒`1/2` b ( PX +PY)

⇒`1/2` b h

⇒`(1/2) times 20`

⇒10 units.

**Example3:**ABCD is a cyclic trapezium with AB parallel DC and AB diameter of circle. If angle CAB = `30^o`, then angle ADC will be?

**Solution:**According to ques, figure will be as follows:

- Angle subtended by diameter is always `90^o`.
- Sum of angles of triangle = `180^o`.
- Sum of opposite angles = `180^o`

`angle` BAC = `30^o`

Therefore,

**Example4:**Two side of plot measures 30m and 22m and angle between them is `90^o`. The other two sides measures 24m and the three remaining angles are not right angles. Find the area of plot.

**Solution:**Figure becomes:

Given BC=CD

ReplyDeleteTherefore line drawn from C to BD gives right angles.

Could you please explain in detail?