1.

From a point P outside the circle, two tangents are drawn to the circle to intersect the circle in points Q and R, respectively. It is found that PQ = PR = 20 cm. The radius of circle is 5 cm. If M is centre of circle, then find the area of quadrilateral PQMR (in square cm)?1). 80 cm22). 72 cm23). 100 cm24). 108 cm2

Answer»

Solution:

The length of the TWO tangents from point P(outside the circle) to points on circle Q and R is given by ,

PQ = PR = 20 cm 

It is given that centre of the circle is 'M' and the radius is 5 cm.

The length of any point on the circle to the centre equals the radius of the circle. So, MQ = MR = 5 cm.

We have to find the area of the quadrilateral PQMR.

We now know all the sides of the quadrilateral PQMR,that is 

PQ = 20 cm = a

QM = 20 cm = B

MR = 5 cm = c 

RP = 5 cm = d

Brahmagupta's formula to find the area of quadrilateral with all four sides a ,b , c and d is given by

A = [(s - a)(s - b)(s - c)(s - d)]^1/2

where s =( a + b + c + d)/2

s = (20 + 20 + 5 + 5)/2

s = 50/2

s = 25

So, A = [(25 - 20)(25 - 20)(25 - 5)(25 - 5)]^1/2

A = [ 5 × 5 × 20 × 20 ]^1/2

A = (10,000)^1/2

A = 100 sq.cm 

Therefore the correct option is 3).100 sq.cm.

 

 

 



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