Geometry - Study Mode
[#76] Two circles of radii 15 cm and 10 cm intersect each other and the length of their common chord is 16 cm. What is the distance (in cm) between their centres?
Correct Answer
(C) $$6 + sqrt {161} $$
Explanation
Solution: So, OO' = $$6 + sqrt {161} $$
[#77] The lengths of two sides of a parallelogram are 3 cm and 10 cm. What is the sum of the squares of the diagonals of the parallelogram?
Correct Answer
(A) 218 cm 2
Explanation
Solution: AC 2 + BD 2 = 2(AB 2 + BC 2 ) AC 2 + BD 2 = 2(10 2 + 3 2 ) = 218
[#78] In the given figure, PQR is a triangle in which angle P : angle Q : angle R = 3 : 2 : 1, and PR is perpendicular to RS. What will be the measure of angle TRS?
Correct Answer
(A) 60°
Explanation
Solution: P : Q : R = 3 : 2 : 1 3 + 2 + 1 = 6u → 180° 1u → 30° P = 90° xa0 ∠PRS = 90° Q = 60° R = 30° ∠P + ∠Q = ∠PRT 90° + 60° = ∠PRS + ∠TRS 150° = 90° + ∠TRS ∠TRS = 60°
[#79] Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circles 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?
Correct Answer
(B) 3.75
Explanation
Solution: $$eqalign{
& { ext{In }}Delta {O^1}CP cr
& {O^1}P = sqrt {{{20}^2} + {{15}^2}} = 25{ ext{ cm}} cr
& OP = 25 - 15 - r = 10 - r cr
& { ext{In }}Delta OPD,& ,Delta {O^1}CP cr
& frac{{OP}}{{{O^1}P}} = frac{{OD}}{{{O^1}C}} cr
& frac{{10 - r}}{{25}} = frac{r}{{15}} cr
& 150 - 15r = 25r cr
& r = frac{{150}}{{40}} cr
& r = 3.75{ ext{ cm}} cr} $$
[#80] XY and XZ are tangents to a circle. ST is another tangent to the circle at the point R on the circle which intersects XY and XZ at S and T respectively, If XY = 9 cm and TX = 15 cm, then RT is:
Correct Answer
(D) 6 cm
Explanation
Solution: XY = 9 cm, TX = 15 cm ⇒ We know Length of tangents drawn from a point to the circle are equal Therefore XY = XZ = 9 cm, TZ = RT TX = 15 cm XZ + ZT = 15 ZT = 15 - 9 = 6 RT = ZT = 6 cm