In parallelogram A BC D , ∠ A = 6 0 ∘ . The angle bisector at B meets C D at E . Circle S 1 of radius r is inscribed in △ ECB , while S 2 is inscribed in trapezoid A BE D . Match the quantities. C

Question

In parallelogram A BC D , ∠ A = 6 0 ∘ . The angle bisector at B meets C D at E . Circle S 1 ​ of radius r is inscribed in △ ECB , while S 2 ​ is inscribed in trapezoid A BE D . Match the quantities. Column I: (A) Radius of S 2 ​ . (B) Distance between centres of S 1 ​ and S 2 ​ . (C) Length of an internal common tangent of S 1 ​ , S 2 ​ . (D) Length CE . Column II: ( p ) 2 3 ​ r (q) ( 3 ​ /2 ) r ( r ) 7 ​ r ( s ) ( 3/2 ) r ( t ) r Column I Column II (A) Radius of S2 (p) 2√3 r (B) Distance between centres of S1 and S2 (q) (√3/2) r (C) Internal common tangent length of S1 and S2 (r) √7 r (D) Length CE (s) (3/2) r; (t) r

TestHub · Accepted Answer

The source gives only an embedded diagram and no written derivation. Using its labelled construction, $r_{2} = 3 r /2$ , the centres are $7 r$ apart, the internal tangent has length $7 r^{2} - (r + 3 r /2)^{2} = (3 /2) r$ , and $CE = 23 r$ . Source schematic is not to scale; verify its geometry in staging.

Mathematics - Circle Question with Solution | TestHub

Options:

Doubts & Discussion

Column I	Column II
(A) Radius of S2	(p) 2√3 r
(B) Distance between centres of S1 and S2	(q) (√3/2) r
(C) Internal common tangent length of S1 and S2	(r) √7 r
(D) Length CE	(s) (3/2) r; (t) r