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In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size ...


Question

In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size of <EHF.

Options

A) 126o

B) 72o

C) 64cmo

D) 32cmo

The correct answer is B.

Explanation:

F = 54\(^{\circ}\) (Alternate triangle angles)
< GHE = F = 54\(^{\circ}\)(Angle between a chord and a tangent = angles in the alternate segment)
Now, < GHE + < EHF + < IHF = 180\(^{\circ}\)(Angles on a straight line)
54\(^{\circ}\) + < EHF + 54\(^{\circ}\)= 180\(^{\circ}\)
< EHF = 180\(^{\circ}\)- 108\(^{\circ}\)
= 72\(^{\circ}\)

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Dicussion (1)

  • F = 54\(^{\circ}\) (Alternate triangle angles)
    < GHE = F = 54\(^{\circ}\)(Angle between a chord and a tangent = angles in the alternate segment)
    Now, < GHE + < EHF + < IHF = 180\(^{\circ}\)(Angles on a straight line)
    54\(^{\circ}\) + < EHF + 54\(^{\circ}\)= 180\(^{\circ}\)
    < EHF = 180\(^{\circ}\)- 108\(^{\circ}\)
    = 72\(^{\circ}\)

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