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Offline Centres

In the given figure, AB, BC and AC touch the circle at L, M and N respectively. If ∠B = 70° and ∠C = 60°, then the measure of ∠LON is:

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140 °

130 °

125 °

100 °

answer is B.

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Detailed Solution

Given:
ABC is a triangle
LMN is a circle.
AB and AC= tangents of the circle.

∠ B = 70 °

∠ C = 60 °

So,

∠ A + ∠ B + ∠ C = 18 0^{\circ}

(By angle sum property of triangle)

∠ A + 70 ° + 60 ° = 180 °

∠ A + 130 ° = 180 °

∠ A = 180 ° - 130 °

∠ A = 50 °

A is intersection point of tangents. Thus, ∠BAC and ∠LON are supplementary.
So,

∠ BAC + ∠ LON = 180 °

50 ° + ∠ LON = 180 °

(

angle BAC = 50 °

)

∠ LON = 180 ° - 50 °

∠ LON = 130 °

Option 2 is correct.

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