Question

Tʰᵉ ˡᵉⁿᵍᵗʰ ᵒᶠ ᵃ ᵗᵃⁿᵍᵉⁿᵗ ᶠʳᵒᵐ ᵃ ᵖᵒⁱⁿᵗ A ᵃᵗ ᵃ ᵈⁱˢᵗᵃⁿᶜᵉ ᵒᶠ 5ᶜᵐ ᶠʳᵒᵐ ᶜᵉⁿᵗʳᵉ ⁱˢ 4ᶜᵐ.Fⁱⁿᵈ ᵗʰᵉ ʳᵃᵈⁱᵘˢ ᵒᶠ ᵗʰᵉ ᶜⁱʳᶜˡᵉ.

ᑎO ՏᑭᗩᗰᗰIᑎᘜ​

Answer 1

Step-by-step explanation:

LetAT be the tangent drawn from a point A to a circle with centre

O and OA=5 cm and AT=4 cm.

Since tangent at a point is

perpendicular to the radius through the point of contact

∴OT⊥AT

∴ from right angled △OAT

it is based on pythogras theorem

hope u like it

Answer 2

The radius of circle is 3 cm. If the length of tangent from a distance of 5 cm from centre is 4 cm.

Given:

• A circle
• A tangent of length 4 cm.
• Point A is 5cm apart from the centre.

To find:

• Find the radius of circle.

Solution:

Concept to be used:

1. The point of intersection of radius and tangent form right angle.
2. Apply Pythagoras theorem.

Step 1:

Draw the situation and labelled it.

As shown in attached figure.

Let the point where tangent touches circle is P.

Step 2:

∆OAP is right angle triangle is right angle at P.

Two sides are already known.

Hypotenuse (AO)=5 cm

Let

Base(PA)= 4 cm

Perpendicular (OP)=?

Apply Pythagoras theorem

Hypotenuse²=Base²+ Perpendicular²

AO² = PA² +OP²

$25 = 16 + OP²$

or

$OP² = 25 - 16$

or

$OP² = 9$

or

$\bf OP = 3$

Thus,

Radius of circle is 3 cm.

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