Geometry - Study Mode

[#91] ln the given figure, from the point P two tangents PA and PB are drawn to a circle with centre O and radius 5 cm. From the point O, OC and OD are drawn parallel to PA and PB respectively. If the length of the chord AB is 5 cm. then what is the value (in degrees) of ∠COD?
Correct Answer

(B) 120

Explanation

Solution: So, ΔAOB is an equilateral triangle So, ∠APB + ∠AOB = 180° ∠APB = 120° So PA and PB are parallel to OC and OD So ∠APB = ∠COD ∴ ∠COD = 120°

[#92] In a circle with centre O, AB is the diameter. P and Q are two points on the circle on the same side of the diameter AB. AQ and BP intersect at C. If ∠POQ = 54°, then the measure of ∠PCA is:
Correct Answer

(A) 63°

Explanation

Solution: 2α + 2β + 54° = 180° 2(α + β) = 126° α + β = 63° ∠PCA = ∠CAB + ∠CBA = α + β = 63°

[#93] The perimeter of right-angle triangle is 60 cm and its hypotenuse is 26 cm. What is the area (in cm 2 ) of the triangle?
Correct Answer

(D) 120

Explanation

Solution: Hypotenuses = 26 cm Perimeter = 60 cm Using by pythagoras triplet - 5, 12, 13 13 unit → 26 cm 1 unit → 2 cm Area of triangle = $$frac{1}{2}$$ × 10 × 24 = 120 cm 2

[#94] In an isosceles ΔABC, AD is the median to the unequal side meeting BC at D. DP is the angle bisector of ∠ADB and PQ is drawn parallel to BC meeting AC at Q. Then the measure of ∠PDQ is
Correct Answer

(B) 90°

Explanation

Solution: ∠PDQ = 45° + 45° = 90°

[#95] Two concentric circles are of redii 13 cm and 5 cm. The length of the chord of the larger circle
which touches the smaller circle is:
Correct Answer

(A) 24 cm

Explanation

Solution: AM = 12 AB = 2 × 12 = 24 cm