Mathematics
In figure given below, O is the centre of the circle, use the given information to find the value of x:
Circles
1 Like
Answer
PA = PB (Given)
⇒ ∠PAB = ∠PBA = x (let) [Angles opposite to equal sides of a triangle are always equal]
As we know that the angle subtended by a diameter at any point on the circumference of a circle is a right angle (90°).
⇒ ∠APB = 90°
In ΔAPB, using angle sum property
⇒ ∠PAB + ∠PBA + ∠APB = 180°
⇒ x + x + 90° = 180°
⇒ 2x = 180° - 90°
⇒ 2x = 90°
⇒ x =
⇒ x = 45°
⇒ ∠PAB = ∠PBA = 45°
Hence, the value of x = 45°.
Answered By
3 Likes
Related Questions
In the following figure, PQ and PR are the tangent to the circle with centre O. Line segment AC touch the circle at point B.
(i) State the relation between tangent PQ and PR.
Also show that:
(ii) PQ = PA + AB
(iii) PR = PC + CB
(iv) PQ + PR = Perimeter of ΔPAC.
From an external point P, the tangent PA is drawn to the circle with centre O.
(i) If OP = 20 cm and tangent PA = 16 cm find the diameter of the circle.
(ii) If diameter of the circle is 20 cm and tangent PA = 24 cm, find the length of OP.
In figure given below, O is the centre of the circle, use the given information to find the value of x:
In figure given below, O is the centre of the circle, use the given information to find the value of x:
