Advertisements
Advertisements
प्रश्न
Point P (2, -7) is the center of a circle with radius 13 unit, PT is perpendicular to chord AB and T = (-2, -4); calculate the length of: AT
Advertisements
उत्तर
Given, radius = 13 units
PA = PB = 13 units
Using distance formula,
PT = `sqrt((-2 -2)^2 + (-4 + 7)^2)`
= `sqrt(16 + 9)`
= `sqrt(25)`
= 5
Using Pythagoras theorem in Δ PAT,
AT2 = PA2 - PT2
AT2 = 169 - 25
AT2 = 144
AT = 12 units.
APPEARS IN
संबंधित प्रश्न
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
The distance between the points (3, 1) and (0, x) is 5. Find x.
Given A = (3, 1) and B = (0, y - 1). Find y if AB = 5.
Calculate the distance between A (5, -3) and B on the y-axis whose ordinate is 9.
The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.
Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.
