Geometry - Study Mode

[#131] A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and AD at the points P, Q, R and S, respectively, and ∠B = 90°. If AD = 24 cm, AB = 27 cm and DR = 6 cm, then what is the circumference of the circle?
Correct Answer

(B) 18π

Explanation

Solution: In $$square $$ POQB, PBOQ is a square because PB = BQ PB = OQ So, BQ = OQ = OP = r Circumference = 2πr = 2π × 9 = 18π

[#132] In a circle, O is the centre of the circle. Chords AB and CD intersect at P. If ∠AOD = 32° and ∠COB = 26°, then the measure of ∠APD lies between:
Correct Answer

(B) 26° and 30°

Explanation

Solution: ∠AOD = 2∠ABD ∠COB = 2∠CDB ∠AOD + ∠COB = 2(∠ABD + ∠CDB) 32° + 26° = 2∠APD ∠APD = 29°

[#133] Let ΔABC and ΔABD be on the same base AB and between the same parallels AB and CD. Then the relation between areas of triangles ABC and ABD will be
Correct Answer

(D) ΔABC = ΔABD

Explanation

Solution: The height of ΔABC and ΔABD are same and have same base. ∴ Area ΔABC = Area ΔABD

[#134] In a triangle ABC, D is a point on BC such that $$frac{{{ ext{AB}}}}{{{ ext{AC}}}} = frac{{{ ext{BD}}}}{{{ ext{DC}}}}.$$ xa0 If ∠B = 68° and ∠C = 52°, then measure of ∠BAD is equal to:
Correct Answer

(D) 30°

Explanation

Solution: If $$frac{{{ ext{AB}}}}{{{ ext{AC}}}} = frac{{{ ext{BD}}}}{{{ ext{DC}}}}$$ xa0 then AD is bisector of ∠A. ∠A = 180° - (68° + 52°) ∠A = 60° ∠BAD = $$frac{{{{60}^ circ }}}{2}$$ = 30°

[#135] Two chords AB and CD of a circle with centre O intersect at P. If ∠APC = 40°. Then the value of ∠AOC + ∠BOD is
Correct Answer

(C) 80°

Explanation

Solution: x + y = 40° 2x + 2y = 80° ∠AOC + ∠BOD = 80°