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Two circles of centers O1 and O2 of radius 5 cm and 8 cm respectively touch each other externally. From the center of bigger circle, a tangent is drawn at point P of smaller circle, then what will be the area of ∆PO1O2?

Two circles of centers O1 and O2 of radius 5 cm and 8 cm respectively touch each other externally. From the center of bigger circle, a tangent is drawn at point P of smaller circle, then what will be the area of ∆PO1O2? Correct Answer 30 cm<sup>2</sup>

GIVEN:

Radii of 2 circles are 5 cm and 8 cm.

CONCEPT:

Apply the secant theorem:

When a tangent and a secant is drawn from an external point to the circle:

The product of the lengths of the secant segment and its external segment is equal to the square of the length of the tangent segment.

FORMULA USED:

PO22 = O2Q × (O2Q + 2O1Q)

Area of triangle = 1/2 × base × height

CALCULATION:

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From the secant theorem:

PO22 = 8 × (8 + 10)                   (Diameter of smaller circle is considered as per the secant rule)

⇒ PO22 = 144

⇒ PO2 = 12 cm

⇒ PO1 = 5 cm

∴ Area of ∆PO1O2 = (1/2) × 5 × 12 = 30 cm2

Mistake Point:

The formula is PO22 = O2Q × (O2Q + 2O1Q)

(Not PO22 = O2Q × QO1) : May be confusing.

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