Question

two concentric circles are of diameter 20 and 52 cm. find the length of the line which is a tangent to the smaller circle and chord to the bigger circle.

Answer 1

Answer:

48cm

Step-by-step explanation:

Now I have upload a picture do refer it,

Now, There are two concentric circles with centre O and Radius 20/2 = 10cm and 52/2 = 26cm

Let the chord be AB

And Now let's join O to AB at C such that it is perpendicular to AB and O to A and B

so now we have two triangles

Here

OA = OB = 26cm ( Radii of the same circle)

Also, we have learned that if a perpendicular from the centre is drawn it will bisect it the chord (Theorem)

(bisect means divide into equal halves)

Therefore, AC = BC

also, OC is the radius of the smaller circle

OC = 10cm

we can find AC using Pythagorus theorem

a² + b² = c²

In triangle AOC,

OC² + AC² = OA²

AC² = OA² - OC²

AC² = 26² - 10²

AC² = 676 - 100 = 576

AC = √576 = 24cm

Now AB = AC + BC

AB = AC + (AC) ( because AC = BC)

AB = 2 × AC

AB = 2 × 24 = 48cm

so the chord is 48cm long....

Hope you understood it........All the best.