A problem by Shreya Khandelwal

Level pending

I am standing at a point Q outside a circular park. The length of tangent from Q to the park is 24m. Also distance of my position to the centre of the park is 25m. Find the radius of the park.


The answer is 7.

Shreya Khandelwal by Shreya Khandelwal , 23

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2 solutions

Akshay Paunikar
Jan 4, 2014

This was quite simple let center of circle be O and the position of person be A We know the length of tangent(Q)=24m and distance of person's position to the centre circle(AO)=25m This forms right angled triangle AOQ and we need to find lenght of side OQ which is opposite to angle OAQ length OQ= Root(AO^2-AQ^2) Answer we get is 7

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Shiven Bholwani
Jan 3, 2014

Let P be the center of the circle and R be the point where tangent meets the circle. After joining points PR we get a right angle triangle.

Then, 

        PQ = 25,

        RQ = 24

        PR = ? = radius

By using Pythagoras theorem, we get

PQ^2 = PR^2 + QR^2

25^2 = PR^2 + 24^2

PR = Sq.Root(25^2 - 24^2)

PR = Sq.Root(625 - 576)

PR = Sq.Root(49)

PR = 7 meter = RADIUS

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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