$D$ is the mid point of side $B C$ and $A E \perp B C$. If $B C=a, A C=b, A B=c, E D=x, A D=p$ and $A E=$ $h$, prove that $c^2=p^2-a x+\frac{a^2}{4}$
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Geometry question types
74 questions across 2 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
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Sample Questions
Geometry questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$D$ is the mid point of side $B C$ and $A E \perp B C$. If $B C=a, A C=b, A B=c, E D=x, A D=p$ and $A E=$ $h$, prove that $b^2+c^2=2 p^2+\frac{a^2}{2}$
View full solution →ABC is a triangle in which AB = AC. Points D and E are points on the side AB and AC respectively such that AD = AE. Show that the points B, C, E and D lie on a same circle
O is any point inside a triangle ABC. The bisector of ∠AOB, ∠BOC and ∠COA meet the sides AB, BC and CA in point D, E and F respectively. Show that AD × BE × CF = DB × EC × FA
If BD ⊥ AC and CE ⊥ AB, prove that ∆AEC ~ ∆ADB
Two circles intersect at A and B. From a point, P on one of the circles lines PAC and PBD are drawn intersecting the second circle at C and D. Prove that CD is parallel to the tangent at P.
An Emu which is 8 feet tall is standing at the foot of a pillar which is 30 feet high. It walks away from the pillar. The shadow of the Emu falls beyond Emu. What is the relation between the length of the shadow and the distance from the Emu to the pillar?
A man whose eye-level is 2 m above the ground wishes to find the height of a tree. He places a mirror horizontally on the ground 20 m from the tree and finds that if he stands at a point C which is 4 m from the mirror B, he can see the reflection of the top of the tree. How height is the tree?
$D$ is the mid point of side $B C$ and $A E \perp B C$. If $B C=a, A C=b, A B=c, E D=x, A D=p$ and $A E=$ h, prove that $b^2=p^2+a x+\frac{a^2}{4}$
View full solution →Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of $\frac{20 km }{ hr }$ and the second train travels at $\frac{30 km }{ hr }$. After 2 hours, what is the distance between them?
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