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Offline Centres

In the given figure, two circles having centers A and B touch externally at point C. DE and GH are two tangents at points $D$ and $G$ respectively. If $∠ ACD =$ $20 °,$ find the measure of $∠ CGH$

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30 o

70 o

60 o

90 o

answer is B.

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Detailed Solution

Given that two circles having centers A and B touch externally at point C.
We have to find the measure of

∠ CGH .

The angle made by the intersection of the radial line and tangent at the circle is

90 o

Join AD, BC, and BG.
Question Image

Since,

∠ A C D

and

∠ B C G

are vertically opposite angles, so,

∠ A C D = ∠ B C G

It is given that,

∠ A C D = 20 °

. This implies,

∠ B C G = 20 °

. Since angle opposite to the equal sides is equal. So,

∠ B C G = ∠ B G C = 20 °

. As the angle made by the intersection of the radial line and tangent at the circle is

90 o

. So,

∠ B G C + ∠ C G H = 90 ° ⇒ ∠ C G H = 90 ° − 20 ° ⇒ ∠ C G H = 70 °

The angle is,

∠ C G H = 70 °

Therefore, the correct option is 2.

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