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Two tangents to a circle having center at O meet the circle at point
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16 Jan 2025, 04:11
16 Jan 2025, 04:11
Expert Reply
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Question Stats:
50% (02:18) correct
50% (01:26) wrong based on 2 sessions
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Two tangents to a circle having center at O meet the circle at points A and B. The two tangents meet each other at a point C outside the circle. Angle ACB is 50o
Quantity A |
Quantity B |
Angle AOB |
110° |
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Re: Two tangents to a circle having center at O meet the circle at point
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23 Feb 2025, 02:07
23 Feb 2025, 02:07
Expert Reply
We are given that two tangents $\(\mathrm{AC} \& \mathrm{BC}\)$, intersect outside the circle at C and form an angle of 50 degrees (As shown in the figure below)
As radius is always perpendicular on tangent, we get angle $\(\mathrm{OAC}=\)$ angle $\(\mathrm{OBC}=90\)$ degree .
Now in quadrilateral AOBC , we get angle $\(\mathrm{AOB}=360^{\circ}-\left(50^{\circ}+90^{\circ}+90^{\circ}\right)=360^{\circ}-230^{\circ}=130^{\circ}\)$ (Sum of the angles of a quadrilateral is 360 degrees)
Hence, column $\(A\)$ has higher quantity when compared with column $\(B\)$, so the answer is (A).
As radius is always perpendicular on tangent, we get angle $\(\mathrm{OAC}=\)$ angle $\(\mathrm{OBC}=90\)$ degree .
Now in quadrilateral AOBC , we get angle $\(\mathrm{AOB}=360^{\circ}-\left(50^{\circ}+90^{\circ}+90^{\circ}\right)=360^{\circ}-230^{\circ}=130^{\circ}\)$ (Sum of the angles of a quadrilateral is 360 degrees)
Hence, column $\(A\)$ has higher quantity when compared with column $\(B\)$, so the answer is (A).
gmatclubot
Re: Two tangents to a circle having center at O meet the circle at point [#permalink]
23 Feb 2025, 02:07
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