Question

In the figure, m is the centre of the ciecde and seg KL is a temgent segment. If mk=12, KL=615 then find lupadius of the circle u measure of LK and cm .
step by step explaination​

Answer 1

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(1) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

∴∠MLK=90o

In right ΔMLK,

MK2=ML2+LK2

⇒ML=MK2−LK2

⇒ML=(12)2−(63)2

⇒ML=144−108

⇒ML=36=6cm

Thus, the radius of the circle is 6cm.

(2) In right ΔMLK,

tan∠K=KLML

⇒tanK=636=31

⇒tanK=tan30o

⇒tanK=30o

Using angle sum property, we have

∠K+∠L+∠M=180o

⇒30o+90o+∠M=180o

⇒120o+∠M=180o

⇒∠M=180o−120o=60o

Thus, the measures of ∠K and 

∠M are 30o and 60, respectively