Question

From a point Q the length of the tangent to a circle is 24 cm and radius of circle is 7 cm then the distance of a Q from center is:​

Answer 1

Answer:

Distance of Q from center= 25 cm

Step-by-step explanation:

Given:-

• From a point Q the length of the tangent to a circle is 24 cm.
• Radius of circle is 7 cm.

We are supposed to find out the distance of point Q from the center of the circle respectively.

• We know that the radius of a circle is always perpendicular to the tangent at the point of contact.

$\therefore$ $\angle$ OPQ = 90°

Also,

• OP = 7cm {Given}

• PQ = 24cm {Given}

∆ OPQ is a right angle triangle.

• In order to find out OP we can use the Pythagoras property of a right angled triangle.

The Pythagoras theorem states that;

• “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides"
• ${H}^{2}$ = ${B}^{2}$ + ${P}^{2}$

Hence, using this in ∆ POQ we have

${H}^{2}$ = ${24}^{2}$ + ${7}^{2}$

${H}^{2}$ = 576 + 49

$\implies$ H = $\sqrt{625}$

$\implies$ H = 25 cm.