Question 43

In the given figure. triangle ABC is drawn such that AB is tangent to a circle at A whose radius is10 cm and BC passes through centre of the circle. Point C lies on the circle. If BC = 36 cm and AB = 24cm .then what is the area $$(in cm^2)$$ of triangle ABC?

Solution

In right angle triangle OAB

$$\sin$$B = $$\dfrac{OA}{OB} = \dfrac{10}{26} = \dfrac{5}{13}$$

In triangle ABC, Area of triangle = $$\dfrac{1}{2}*AB*BC\sin$$B

$$\Rightarrow$$ $$\dfrac{1}{2}$$*24*36*$$\dfrac{5}{13}$$ = 166.15

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