In figure 3.83, M is the centre of the circle and seg KL is a tangent segment. If MK = 12, KL = 6√(3) then find - (1) Radius of the circle. (2) Measures of ∠ K and ∠ M . Figure: L is the point of contact on the circle; seg ML is a radius and K is outside the circle.

Answer: (1) Radius = 6 (2) ∠ K = 30^° , ∠ M = 60^° (1) ∠ MLK = 90^° (tangent ⊥ radius). In right-angled triangle MLK : ML² = MK² - KL² = 144 - 108 = 36 ML = 6 (2) ML = 6 = 1/2 MK. In a right-angled triangle, if a side is half the hypotenuse, the angle opposite it is 30^° . So ∠ K = 30^° and ∠ M = 90^° - 30^° = 60^°

In figure 3.83, M is the centre of the circle and seg KL is a tangent segment. If MK = 12, KL = 6√3 then find - (1) Radius of the circle. (2) Measures of ∠K and ∠M.

In figure 3.83, M is the centre of the circle and seg KL is a tangent segment. If MK = 12, KL = \(6\sqrt{3}\) then find -

(1) Radius of the circle. (2) Measures of \(\angle K\) and \(\angle M\).

Figure: L is the point of contact on the circle; seg ML is a radius and K is outside the circle.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

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Answer: (1) Radius = 6 (2) \(\angle K = 30^\circ\), \(\angle M = 60^\circ\)

(1) \(\angle MLK = 90^\circ\) (tangent ⊥ radius). In right-angled \(\triangle MLK\):

\[ML^2 = MK^2 - KL^2 = 144 - 108 = 36\] \[ML = 6\]

(2) ML = 6 = \(\frac{1}{2}\) MK. In a right-angled triangle, if a side is half the hypotenuse, the angle opposite it is \(30^\circ\). So \(\angle K = 30^\circ\) and

\[\angle M = 90^\circ - 30^\circ = 60^\circ\]

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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In figure 3.83, M is the centre of the circle and seg KL is a tangent segment. If MK = 12, KL = 6√3 then find - (1) Radius of the circle. (2) Measures of ∠K and ∠M.

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