Question

Point p(2,-7) is the centre of a circle with radius 13 units, PT is perpendicular to chord AB and T = (-2,-4). Calculate the length of AT and AB

Answer 1

The length of AT is 12 units and AB is 24 units.

Explanation:

Given : Point P(2,-7) is the centre of a circle with radius 13 units, PT is perpendicular to chord AB.

It means Δ APT is a right triangle.

By distance formula , the distance between point P ant T would be

$PT=\sqrt{(-2-2)^2+(-4-(-7))^2}\\\\=\sqrt{(-4)^2+(3)^2} =\sqrt{25}=5$

i.e. PT= 5 units

By Pythagoras theorem , we have

$AP^2=AT^2+PT^2\\\\=13^2=AT^2+5^2\\\\ AT^2=169-25=144\\\\ AT=12\ units$

Also, The perpendicular line on chord divide it into two equal parts , therefore , the length of chord AB= 2 (AT) = 2(12)= 24 units.

∴ The length of AT is 12 units and AB is 24 units.

#Learn more :

P is the centre of the circle and it's radius is 10cm . Distance of a chord AB from the centre is 6 cm . Find the length of chord AB

https://brainly.in/question/7058757

Answer 2

Answer:

AT=12unit AB=24unit

Step-by-step explanation:

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