In the given figure, AD and AE are the tangents to a circle with centre O and BC touches the circle at F. If perimeter of triangle ABC = 12cm , then AE = ?
Answers
If AD and AE are tangents to a circle, BC touches the circle at F and perimeter of triangle ABC = 12 cm then AE is 6 cm.
Step-by-step explanation:
Referring to the figure attached below and according to the question we have
AD and AE tangents to the circle with centre O.
BC is another tangent to the circle which touches the circle at point F.
We know that the tangents drawn from an external point to a circle are equal, therefore, we have
CF = CD ….. (i) [tangents from point C]
BF = BE ….. (ii) [tangents from point B]
AE = AD ….. (iii) [tangents from point A]
It is also given that the perimeter of ∆ ABC = 12 cm
And we know,
Perimeter of ∆ ABC = AB + BC + AC
∴ AB + BC + AC = 12
⇒ (AE - BE) + (BF + CF) + (AD - CD) = 12 …… [from the figure]
from (i), (ii), (iii) we get
⇒ 2 AE = 12
⇒ AE = 12/2
⇒ AE = 6 cm
Thus, the length of AE is 6 cm.
----------------------------------------------------------------------------
Also View:
Pq and pt are tangents to a circle with centre o and radius 5 cm if pq = 12 cm then prove that the perimeter of the quadrilateral pqot is 34 cm
https://brainly.in/question/12318850
Find the length of the tangent to the circle with center O and radius 6cm from a point P such that OP is 10cm
https://brainly.in/question/7816560
Ab is tangent to a circle with center P touching the circle at B. PA intersects the circle at M. if AB=35cm and AM=25cm, find the diameter
https://brainly.in/question/13268355
The value of AE is 6cm.
Step-by-step explanation:
Consider the provided information.
Perimeter of triangle ABC = 12cm
Perimeter of Triangle ABC = AB + BC + AC
12 = AB + BC + AC
12 = AB + FB + CF + AC
Tangents drawn from an external point to a circle are equal.
BE = FB
Similarly CF = CD
Therefore,
12 = AB + BE + CD+ AC
12 = AE + AD
Tangents drawn from an external point to a circle are equal.
AE = AD
12 = 2 AE
AE = 6
Hence, the value of AE is 6cm.
#Learn more
Prove that tangent drawn from an external point to circle are equal
https://brainly.in/question/8241062
