Question

In the following figure, a quadrilateral LMNO circumscribes a circle with centre C. ∠O = 90°, LM = 25 cm, LO = 27 cm and MJ = 6 cm. Calculate the radius of the circle.

Answer 1

Given: ∠O = 90°, LM = 25 cm, LO = 27 cm, MJ = 6 cm

Tangents drawn from an exterior point to a circle have the same radius.

So, LI = LH

MI = MJ

NJ = NG

And OH = OG

Now, MI = MJ = 6 cm  ......[Given]

So, LI = LM – MI

= 25 – 6

= 19 cm

So, LI = LH = 19 cm

Similarly, OH = LO – LH

= 27 – 19

= 8 cm

The tangent to a circle is perpendicular to the radius through the point of contact.

So, ∠CHO = ∠CGO = 90°

Also, ∠O = 90°  ......[Given]

So, ∠GCH = 90°

As a result, CHOG is a square.

So, CH = CG = OH = 8 cm

As a result, the radius of the circle is 8 cm.