Given: AB tangent to circle O at B, and secant through point A intersect the circle at points C and D. Find CD, if
2 answers:
Answer:
CD = 6 cm.
Step-by-step explanation:
In the figure attached AB is the tangent of circle O at point B. A secant through point A intersect the circle at C and D.
mAB = 4cm and mAC = 2cm
We have find the length of CD.
By the theorem of secant and tangent
AB² = AC×AD
Here AC = 2 cm
and AD = AC + CD = (2 + CD)
Now we replace the values in the formula
4² = 2(2 + CD)
16 = 4 + 2.CD
2.CD = 16 - 4 = 12
Therefore CD = 6 cm is the answer.
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Answer:
Step-by-step explanation:
In the diagram shown, the measure of angle 1 is oppositely directed to angle 2 and oppositely directed angles are equal.
Hence <1 = <3
Given < 1 = 3x-1 and <3 = 2x+9
Hence 3x-1 = 2x+9
collect like terms
3x-2x = 9+1
x = 10°
Since <1 = 3x-1
on substituting x = 10
<1 = 3(10)-1
<1 = 30-1
<1 = 29°
<1+<2 = 180 (angle on a straight line)
29+<2 = 180
<2 = 180-29
<2 = 151°
Similarly, on substituting x = 10 into <3
<3 = 2x+9
<3 = 2(10)+9
<3 = 20+9
<3 = 29°
<3+<4 = 180 (angle on a straight line)
29+<4 = 180
<4 = 180-29
<4 = 151°
