PA AND PB ARE TANGENTS SUCH THAT PA = 9 CM AND ANGLE APB =60. FIND THE LENGTH OF THE CHORD AB
Answers
The length of the chord AB is 9 cm.
Step-by-step explanation:
It is given that,
PA and PB are tangents to a circle from external point P touching the circle at A and B .
PA = 9 cm
∠APB = 60°
We know that if two tangents are drawn to a circle from one external point, then they have equal tangent segments.
∴ PA = PB = 9 cm
⇒ ∠PBA = ∠PAB ….. [angles opposite to equal sides are equal] ….. (i)
Now consider ΔPAB and applying the angle sum property, we get
∠PBA + ∠PAB + ∠APB = 180°
⇒ ∠PBA + ∠PAB + 60° = 180°
⇒ 2 * ∠PBA = 180° - 60° …… [from eq. (i)]
⇒ 2 * ∠PBA = 120°
⇒ ∠PBA = 120°/2
⇒ ∠PBA = 60°
∴ ∠PBA = ∠PAB = ∠APB = 60°
Since all the 3 angles of ΔPAB is equal to 60°, therefore, we get that ΔPAB is an equilateral triangle.
We know that all the sides of an equilateral triangle are equal to each other.
∴ PA = PB = AB = 9 cm
Thus, the length of the chord AB of the given circle is 9 cm.
--------------------------------------------------------------------------------------------------
Also View:
If two tangents are inclined at an angle of 60 degree of a circle with radius 6 cm and the length of each tangent is ?
https://brainly.in/question/10615727
If AP and AQ are the two tangents a circle with centre O so that ∠POQ = 110°, then ∠PAQ is equal to(a) 60° (b) 70° (c) 80° (d) 90° ?
https://brainly.in/question/5483681
