(a) In the given figure, PAB is a secant and PT a tangent to the circle with centre O. If LATP= 40
PA = 9 cm and AB = 7 cm.
Find :
(1) LAPT
(ii) Length of PT
Answers
(i) ∠APT = 50°
(ii) Length of PT = 9 cm
Solution:
BT is a diameter of a circle.
Angle subtended by a diameter or a semicircle on any point of circle is 90°.
∠BAT = 90°
Sum of the adjacent angles in a straight line = 180°
∠BAT + ∠TAP = 180°
90° + ∠TAP = 180°
∠TAP = 180° – 90°
∠TAP = 90°
In ΔPAT,
Sum of the angles of the triangle = 180°
∠PAT + ∠ATP + ∠APT = 180°
90° + 40° + ∠APT = 180°
130° + ∠APT = 180°
∠APT = 180° – 130°
∠APT = 50°
(ii) P is an external point.
PA and PT are tangents drawn from point P.
Length of PA = 9 cm
Lengths of tangents drawn from an external point to a circle are equal.
Length of PT = Length of PA
Length of PT = 9 cm
To learn more...
1. In the following figure PAB is a secant and PT is the tangent to the circle If PT=5 cm and PA=3cm then find the measurement of AB
https://brainly.in/question/2426335
2. In the figure , PAB is a secant and PT a tangent to the circle with centre O . if angle TAP =40°, PA = 9cm and AB=7cm.
https://brainly.in/question/2426335
Answer:
Please refer to the image
