Question

A tangent line to a circle is a line that intersects the circle at exactly one point. (It appears to brush the edge of a circle). A point of tangency is the point where a tangent line intersects with a circle. Common external tangents do not intersect the segment that has its endpoints on the centres of the two circles. Common internal tangents intersect the segment that has its endpoints on the centres of the two circles. The dotted line represents the line segment that has its endpoints on the centres of the sun and the moon.

The drawing above shows how the sun, moon, and earth are aligned for a solar eclipse. Identify the tangent lines that partition an area on the earth that experiences a total solar eclipse.
EF and DE
GH and HI
EF and HI
DH and GE

From the above drawing, identify the common external tangents between the sun and the moon.
HI and EF
DH and GE
EF and DE
DE and GH

Answer 1

Step-by-step explanation:

1st answer is EF and HI because these two points are making a total solar eclipse.

2nd answer is DE and GH because these two points are making the common external tangents between the sun and the moon.

Answer 2

Question A) :- The drawing above shows how the sun, moon, and earth are aligned for a solar eclipse.Identify the tangents lines which partition an area on the earth that experiences a total solar eclipse.

Answer :-

• The Pink area, the area between the tangents EF and HI is the area that experiences a total solar eclipse.

Question B) :- From the above drawing, identify the common external tangents between the sun and the moon.

Answer :-

we know that, If a tangent touches the upper surface of both circles, it’s a common external tangent.

So,

• The common external tangent are DE and GH as they do not intersect the red dotted line.

Question c) :- From the above drawing, identify the common internal tangents between the sun and the moon.

Answer :-

we know that, if a tangent crosses from the upper surface of one circle to the lower surface of the other, then that tangent is a common internal tangent.

So,

• The common external tangent are DH and GE as they do intersect the red dotted line.

Question D) :- What is the length of DM in the given picture, if EM = y units, HM = 10 units, GM = (y + 10) units.

(i) 15 units

(ii) 20 units

(iii) 10.5 units

(iv) 10 units

Answer :-

we know that, if two tangent segments are drawn to one circle from the same external point, then they are congruent.

So,

→ EM = HM (same External point M from Moon.)

→ y = 10 units.

now,

→ EG = HG (same External point G from Moon.)

→ EM + GM = HG

→ y + (y + 10) = HG

→ 2y + 10 = HG

→ 2 * 10 + 10 = HG

→ 20 + 10 = HG

→ HG = 30 units.

then,

→ HD = HG (same External point H from Sun.)

→ HM + MD = 30

→ 10 + MD = 30

→ MD = 30 - 10

→ MD = 20 units.

therefore, The length of DM is 20 units. (Option ii) .

Question E) :- What is the measure of ∠DOG in the given picture, if ∠DMG = x° .

(i) 180 °

(ii) ( 180 – x )°

(iii) ( 180 + x )°

(iv) 90°.

Answer :-

→ DO = GO = radius of sun.

→ DM = GM = tangents from sun to external point M .

we know that,

A radius that connects to the tangent is 90°.

Sum of all four angles of a quadrilateral is 360° .

So, in quadrilateral DMGO we have,

∠DMG = x°

∠ODM = ∠OGM = 90° . (DO and GO are radius.)

then,

→ ∠DMG + ∠ODM + ∠OGM + ∠DOG = 360° (Angle sum Property of a quadrilateral.)

→ x° + 90° + 90° + ∠DOG = 360°

→ (x + 180)° + ∠DOG = 360°

→ ∠DOG = 360° - (x + 180)°

→ ∠DOG = 360° - 180° - x°

→ ∠DOG = (180 - x)° Option (ii) (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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