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in Three-dimensional geometry by (52.5k points)

In a triangle PQR, let ∠PQR = 30° and the sides PQ and QR have lengths 103 and 10, respectively. Then, which of the following statement(s) is(are) TRUE? 

(A) ∠QPP = 45°. 

(B) The area of the triangle PQR is 253 and ∠QRP = 120°. 

(C) The radius of the incircle of the triangle PQR is 103 – 15. 

(D) The area of the circumcircle of the triangle PQR is 100π

1 Answer

+1 vote
by (54.8k points)
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Best answer

Answer is (B), (C), (D)

Let us check all four options as follows: 

• Option (A): It is given that

Hence, option (B) is true. 

• Option (C): Now, the radius of in circle is

Therefore, the radius of incircle is

53(2 - 3) = 103 - 15

Hence, option (C) is true. 

• Option (D): Now, the area of the circumcircle is πR2, where

Therefore, the area of circumcircle is

π(10)2 = 100π

Hence, option (D) is correct.

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