Ashifur September 9, 2023 - 17:14
Problem: The length of a tangent from a point A at distance 5cm from the center of the circle is 4cm. Find the radius of the circle.

View all: AGRANI BANK LTD (SO-ADUITOR) WRITTEN QUESTION (MATH) SOLVE | 2018

Correct Answer: 3 cm

Explanation:

let. the tangent AB = 5cmDistance at the point A from the center the circle OA = 4cm

Now drawing a perpendicular from the tangent on the center of the circle OB. we get a right angled triangle $\Delta$AOB

Applying Pythagorean theorem

OA$^{2}$+OB$^{2}$= AB$^{2}$

=> 4$^{2}$+OB$^{2}$=5$^{2}$

=> OB$^{2}$= 25-16

=> OB$^{2}$ = 9 =3$^{2}$

So, OB = 3

The radius of the circle is 3cm.

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