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Q. 28. Prove that, in a triangle, if the square on one side is equal to the sum of squares of the other two sides, then the angle opposite to the first side is a right angle. Using the above, show that in an isosceles triangle ABC with AC = BC, if AB² = 2AC² then ABC is a right triangle.

 Sol.

Part I : See Theorem 4,
Page (xxxii).
Part II : AB² = 2AC²
…(Given)
AB² = AC² + AC²
AB² = AC² + BC²
…[AC = BC (given)]

 Or

Prove that the lengths of tangents drawn from an external point to a circle are equal. Use the above result in the following :

A circle is inscribed in a ΔABC, touching AB, BC and AC at P, Q and R
respectively, as shown in

Fig. 7. If AB = 10 cm,
AR = 7 cm and RC = 5
cm, then find the length of BC.

Mathematics 2009 Question Papers Class X
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